yep a better psu is needed. it would work at a push but you would be risking your whole system, and as we know hp dont build there pc's with the best parts, much the opposite in fact.. the chances are that the psu will have a max stable output of less than 250w and a peak wattage of 300 if your lucky... so yeah a 450w or better would be a much safe option even for that small sub 75w gfx card.
if you go to for a decent (cosair/seasonic and so on) 550w you will be able to put almost any gfx card you want in as you already have a pretty decent bare bones with a 2400 sandy.
if your really wanting to play games look to get the psu as said and maybe a gtx 560ti for medium to high quality on most games.