Still sounds like it's either a phone issue (and if it is, dude, talk about bad luck...you should go buy lotto tickets just in case) or something wrong with your account. Are you sure nothing is getting downloaded automatically from Google Play once you set up your account?
Try this. Since you're already going to reset the phone anyways, reset it, but DON'T LOG IN. Don't sync anything. Just skip the Google Account registration (don't worry, you'll reset it again). Use the phone like that for maybe a day? Half a day? A few hours? Just load one video on it (local file) and play. Try streaming one from the web. Then play the local file again. Rinse and repeat. With this, no account, does it still cease to play videos after a while? No? It's your account and something is going funny when you log in (my guess is some kind of rogue app that downloads with your Play Store sync). Now you can reset and try to figure out your account issue.
It still doesn't play videos after a while? OK, now try this. Re-reset. Skip registration and sync, but this time, ALSO disable WiFi and no SIM Card. (That's right, no data whatsoever). Now load a local movie. Play it. Play it. After the usual time it stops working, does it? Yes? It's the phone; get it replaced...again. No? Rset the phone. Try again. Fails? It's the phone again. No? Enable WiFi and try streaming video. Does it fail after a while? Yes? It's your phone downloading something when connected. No? Now try inserting the SIM. Same thing. Does it fail? Yes, it's the phone downloading something from the carrier. No, then it's definitely your account.