Since you don't tell what motherboard you have and why it is incompatible with a gtx 730, it's difficult to comment. Also what happens with the gt610 is unclear.
But I doubt if a 300 W PSU is up to the task. What one, how many rails?
By the way, if you say "I tried to buy", that implies more or less you couldn't buy it. Then it's understandable that only using the onboard graphics doesn't give good results. Next time don't only try to buy a video card (or a new PSU), but actually do] it.
I dont understand why its so difficult to just buy a video card and play a game. Ive tried buying a geforece gtx 730 but my motherboard isnt compatible with that card. Then i tried buying a gt 610 and now playing a game is actually unbearable.
Games that i am trying to play star wars the old republic, world of warcraft, skyrim, and some other newesh games.
i5 2400 3.10
psu 300 watts
onboard graphics card intel hd family
6 gb of ram