There's probably something wrong with either the psp or the battery. That happened to my friend so she went back to gamestop and returned, telling them about the problem and it was within 7 days so she got a new one. You can try to go back to where you bought it and ask for an exchange. =] Hope everything works out.
router is around 40-60 and memory goes up to 8GB which is around 150ish i think ...i may be wrong but i know you can find 4GB for around 60-90ish~ i have a 2GB which i bought for 30 at amazon...i thought it was a good deal =]