I'd say no unless you hate the 3DS. You'd probably only get like, $100 for it unless it's a limited edition one or something.
I'm not sure what this $300 PC you were looking at has inside of it but... a pre-built at that price probably won't be very promising. I mean, if you wanted to JUST play TF2 sure, that game would run fine on Intel's integrated graphics, but some of the more demanding games would look and probably run like crud. If you raise your budget to about $400 and build your own you can easily build something that will max TF2 (or any other Source engine game) and even play modern titles at 1080p on about medium settings. (Maybe higher if it's optimized well or if you game at resolutions like 720p or 900p)