You are probably missing some Visual Studio Dependencies. Make sure you have the VC Redistributable 2013 (and maybe even 2010) installed. In theory the 32bit versions should be enough, but you can also install the 64bit ones for safety, here are the download links:
https://www.microsoft.com/en-US/download/details.aspx?id=40784
http://www.microsoft.com/en-US/download/details.aspx?id=5555
Here's another log, not sure which one is the newest.
12:53:19: CLR host plugin strings not found, dynamically loading 4 strings
12:53:19: CLRHost::Initialize() attempting to load and start the .NET runtime (null)
12:53:19: CLRHost::Initialize() Found version v2.0.50727 .NET runtime
12:53:19: CLRHost::Initialize() Found version v4.0.30319 .NET runtime
12:53:19: CLRHost::Initialize() attempting to use v4.0.30319 .NET runtime
12:53:19: CLRHost::LoadInteropLibrary() load the assembly plugins\CLRHostPlugin\CLRHost.Interop.dll
12:53:19: CLRHost::LoadPlugins() attempting to load the plugin assembly CLRBrowserSourcePlugin
12:53:20: CLRHost:: Could not find/load browser settings at location C:\Users\Brandon\AppData\Roaming\OBS\pluginData\browser.json
12:53:20: CLRHost::LoadPlugins() successfully added CLR plugin [Type: CLRBrowserSourcePlugin.CLRBrowserSourcePlugin, Name: CLR Browser Source Plugin]
12:53:25: Open Broadcaster Software v0.651b - 32bit (´・ω・`)
12:53:25: -------------------------------
12:53:25: CPU Name: AMD FX(tm)-6300 Six-Core Processor
12:53:25: CPU Speed: 3516MHz
12:53:25: Physical Memory: 4095MB Total, 4095MB Free
12:53:25: stepping id: 0, model 2, family 21, type 0, extmodel 0, extfamily 3, HTT 1, logical cores 6, total cores 3
12:53:25: monitor 1: pos={1920, 0}, size={1366, 768}
12:53:25: monitor 2: pos={0, 0}, size={1920, 1080}
12:53:25: Windows Version: 6.2 Build 9200
12:53:25: Aero is Enabled
12:53:25: -------------------------------
12:53:25: OBS Modules:
12:53:25: Base Address Module
12:53:25: 011E0000 OBS.exe
12:53:25: 68DD0000 OBSApi.dll
12:53:25: 68A00000 CLRHostPlugin.dll
12:53:25: 67870000 DShowPlugin.dll
12:53:25: 67840000 GraphicsCapture.dll
12:53:25: 67810000 NoiseGate.dll
12:53:25: 677F0000 PSVPlugin.dll
12:53:25: 677D0000 scenesw.dll
12:53:25: ------------------------------------------
12:53:25: Adapter 1
12:53:25: Video Adapter: NVIDIA GeForce GT 740
12:53:25: Video Adapter Dedicated Video Memory: 2082140160
12:53:25: Video Adapter Shared System Memory: 2147807232
12:53:25: Video Adapter Output 1: pos={0, 0}, size={1920, 1080}, attached=true
12:53:25: Video Adapter Output 2: pos={1920, 0}, size={1366, 768}, attached=true
12:53:25: =====Stream Start: 2015-03-31, 12:53:25===============================================
12:53:25: Multithreaded optimizations: On
12:53:25: Base resolution: 1280x720
12:53:25: Output resolution: 1280x720
12:53:25: ------------------------------------------
12:53:25: Loading up D3D10 on NVIDIA GeForce GT 740 (Adapter 1)...
12:53:25: ------------------------------------------
12:53:25: Audio Format: 48000 Hz
12:53:25: ------------------------------------------
12:53:25: Audio Channels: 2 Ch
12:53:25: Playback device Default
12:53:25: ------------------------------------------
12:53:25: Using desktop audio input: Speakers (VIA High Definition Audio)
12:53:25: Global Audio time adjust: 0
12:53:25: ------------------------------------------
12:53:25: Using auxilary audio input: Microphone (Yeti Stereo Microphone)
12:53:25: Mic time offset: 1500
12:53:25: ------------------------------------------
12:53:25: Audio Encoding: AAC
12:53:25: bitrate: 128
12:53:26: ------------------------------------------
12:53:26: device: Elgato Game Capture HD,
12:53:26: device id {39F50F4C-99E1-464A-B6F9-D605B4FB5918},
12:53:26: chosen type: UYVY, usingFourCC: false, res: 1280x720 - 1280x720, frameIntervals: 333333-333333
12:53:26: use buffering: true - 0, fourCC: 'UYVY'
12:53:26:
12:53:26: device audio info - bits per sample: 16, channels: 2, samples per sec: 48000, block size: 4
12:53:26: Elgato Game Capture: force buffering with 1 msec
12:53:40: Using directshow input
12:53:40: Scene buffering time set to 700
12:53:40: ------------------------------------------
12:53:40: Video Encoding: x264
12:53:40: fps: 30
12:53:40: width: 1280, height: 720
12:53:40: preset: veryfast
12:53:40: profile: high
12:53:40: keyint: 250
12:53:40: CBR: yes
12:53:40: CFR: yes
12:53:40: max bitrate: 2500
12:53:40: buffer size: 2500
12:53:40: ------------------------------------------
12:53:48: Total frames encoded: 213, total frames duplicated: 0 (0.00%)
12:53:48: Total frames rendered: 238, number of late frames: 0 (0.00%) (it's okay for some frames to be late)
12:53:55:
12:53:55: Profiler time results:
12:53:55:
12:53:55: ==============================================================
12:53:55: video thread frame - [100%] [avg time: 3.293 ms] [children: 51.5%] [unaccounted: 48.5%]
12:53:55: | scene->Preprocess - [44.8%] [avg time: 1.476 ms]
12:53:55: | GPU download and conversion - [6.68%] [avg time: 0.22 ms] [children: 6.23%] [unaccounted: 0.456%]
12:53:55: | | flush - [5.77%] [avg time: 0.19 ms]
12:53:55: | | CopyResource - [0.304%] [avg time: 0.01 ms]
12:53:55: | | conversion to 4:2:0 - [0.152%] [avg time: 0.005 ms]
12:53:55: Convert444Thread - [100%] [avg time: 0.983 ms] [children: 98.8%] [unaccounted: 1.22%]
12:53:55: | Convert444toNV12 - [98.8%] [avg time: 0.971 ms]
12:53:55: encoder thread frame - [100%] [avg time: 2.008 ms] [children: 0.249%] [unaccounted: 99.8%]
12:53:55: | sending stuff out - [0.249%] [avg time: 0.005 ms]
12:53:55: ==============================================================
12:53:55:
12:53:55:
12:53:55: Profiler CPU results:
12:53:55:
12:53:55: ==============================================================
12:53:55: video thread frame - [cpu time: avg 2.56 ms, total 609.375 ms] [avg calls per frame: 1]
12:53:55: | scene->Preprocess - [cpu time: avg 1.575 ms, total 375 ms] [avg calls per frame: 1]
12:53:55: | GPU download and conversion - [cpu time: avg 0.262 ms, total 62.5 ms] [avg calls per frame: 1]
12:53:55: | | flush - [cpu time: avg 0.262 ms, total 62.5 ms] [avg calls per frame: 1]
12:53:55: | | CopyResource - [cpu time: avg 0 ms, total 0 ms] [avg calls per frame: 1]
12:53:55: | | conversion to 4:2:0 - [cpu time: avg 0 ms, total 0 ms] [avg calls per frame: 1]
12:53:55: Convert444Thread - [cpu time: avg 1.095 ms, total 234.375 ms] [avg calls per frame: 1]
12:53:55: | Convert444toNV12 - [cpu time: avg 1.095 ms, total 234.375 ms] [avg calls per frame: 1]
12:53:55: encoder thread frame - [cpu time: avg 2.053 ms, total 437.5 ms] [avg calls per frame: 1]
12:53:55: | sending stuff out - [cpu time: avg 0 ms, total 0 ms] [avg calls per frame: 1]
12:53:55: ==============================================================
12:53:55:
12:53:55: =====Stream End: 2015-03-31, 12:53:55=================================================
12:58:25: =====Stream Start: 2015-03-31, 12:58:25===============================================
12:58:25: Multithreaded optimizations: On
12:58:25: Base resolution: 1280x720
12:58:25: Output resolution: 1280x720
12:58:25: ------------------------------------------
12:58:25: Loading up D3D10 on NVIDIA GeForce GT 740 (Adapter 1)...
12:58:25: ------------------------------------------
12:58:25: Audio Format: 48000 Hz
12:58:25: ------------------------------------------
12:58:25: Audio Channels: 2 Ch
12:58:25: Playback device Default
12:58:25: ------------------------------------------
12:58:25: Using desktop audio input: Speakers (VIA High Definition Audio)
12:58:25: Global Audio time adjust: 0
12:58:25: ------------------------------------------
12:58:25: Using auxilary audio input: Microphone (Yeti Stereo Microphone)
12:58:25: Mic time offset: 1500
12:58:25: ------------------------------------------
12:58:25: Audio Encoding: AAC
12:58:25: bitrate: 128
12:58:25: ------------------------------------------
12:58:25: device: Logitech HD Pro Webcam C920,
12:58:25: device id \\?\usb#vid_046d&pid_082d&mi_00#7&1ef9c96&0&0000#{65e8773d-8f56-11d0-a3b9-00a0c9223196}\{bbefb6c7-2fc4-4139-bb8b-a58bba724083},
12:58:25: chosen type: I420, usingFourCC: false, res: 1280x720 - 1280x720, frameIntervals: 333333-2000000
12:58:25: use buffering: true - 15000000, fourCC: 'I420'
12:58:25: audio device: Disable,
12:58:25: audio device id Disabled,
12:58:25: audio time offset 0,
12:58:25:
12:58:25: Using directshow input
12:58:25: Using bitmap image
12:58:25: ------------------------------------------