Laptop or pc with these very vague needs.

Looking for a cheapish computer to record music and play videogames like P.O.E on high settings and can at least run bioshock 2 or infinite.

Think 2010

ATI mobility radeon hd 3400 256m is what I run the games on now. I am really broke and I am "hopefully" getting a transplant soon, just got on the list and would like let me run, at least P.O.E. So I having something to do.

Not allowed to install anything on my work laptop.

The rest would just be streaming video and normal browsing.

Would not mind a pc, am allowed taking it with me.

Budget wise, do not mind used or refurbished: 100-150, maybe 200. If you could at least point me in the right direction.

Really the benchmark would be to be able to play P.O.E in ok settings with out lag.