I have the same problem in Windows 10. In fact I know I wrote it here somewhere in the support forums but I can't find the related post. It always starts as a background process. I can open it a second time and this time it will open but webcam won't be feeding image to OBS. At this point I have 2 OBS processes running. I can close the first one that didn't work, but that won't fix the webcam for the second.
If however, back at the start, I close the first failed OBS process, and open OBS again after that, it will launch normally no problems, webcam working fine.
Now like I said in the other post, this happens every single time. My current method to open OBS is:
1.- Click the OBS icon - watch the (thinking) blue circle. Nothing happens.
2.- Open Process Manager
3.- Terminate OBS process.
4.- Click OBS again.
5.- OBS is finally opened.
This only occurs the very first time I start OBS after launching the PC.
Which let's face it, it's not an interesting way to start every single time. I reinstalled OBS, problem persisted. reinstalled windows (yes), and problem returned after a couple of days.
Edit: Also, I experienced the same problem with another recording app (not simultaneously with OBS, and no I don't run them together), but they seem to have found a fix in their latest update since it stopped happening for their app (plays.tv)