Just go with the warranty route for now, maybe see if they will put a bigger PSU in there for no extra cost or a few dollars extra.
And yes, I reckon 250watts of power is gonna be stretching it, it's probly struggling. I don't have any reservations about using a generic PSU as long as it has an excess wattage rating.
After the warranty period is over, you can go and buy a midi-tower case with a decent PSU. The slim line micro cases look pretty sweet, but they are very impractical as you have seen; cooling could also be a serious problem with them.
I'm generally not violent, but I feel like slapping every gamer/simmer who buys a Compaq or HP rig! .......but then, I would need a lot of help, wouldn't I
Mind you, at least you seem to have a pretty good Spec and decent basic gear there.
Make the BIOS your friend. Go in there and check it out, manual in hand, become familiar with it, you don't have to change anything at first, just exit without saving if you are not sure about something.
See if you can find out exactly what mainboard you have, and go and research it so you understand what you have bought. Find out what chipset makes it tick, and research the chipset so you know the PC's limits.
Just learn a little at a time. It won't take long to understand it.
1 last tip, buy a quality stick of PC3200 ram, a quality ram stick is one that can be timed at low latencies and remain stable, it doesn't mean expensive.
PC3200 is the same price as PC2700, and if you run it at PC2700 speed, you will be able to decrease the ram timings for performance, if your existing ram will handle it..... but get a good stick now, no good getting another slow one, think ahead to a future upgrade always.