i would just reccomend to get a new power supply then. the psu's that come with cases usually go out with in the first few hours, or they last for a few weeks then go.
and just some inside stuff, my main pc (PC1 in my sig) is running a $15 logisys 350w, and its running great, but ive only had this pc since early jan of this year, it was a new years gift to myself, but this psu runs great. there are its off days when its not acting right, but thats why i have a voltage analyser, so if you can, get yourself a voltage meter, and test the 12v and 5v rails. i havent done it in about a month or so, but the 12v is the yellow wire and black next to it, and 5v is the red wire and the black next to it, the colored wires being the + and blacks being the -
i am unsure on how to test the 3.5v lines, but i guess someone here does...
do you have any freinds that would loan you a psu to test in your rig, or a different psu around, or even can you do a quick swap with a psu in another rig to test it?
btw, what are your average temps in your systm (load and idle)? if you dont know, get a program called speedfan, located at this site
it will also tell you your voltages if your motherboard supports it.
and if your system is full of dust, it might be wise to clean it out, i was getting errors and dusted it and man did it make a diff, quieter, little faster, cooler, and stoped bsod'ing.