What I think the problem is is that the battery is dead. When you use the power switch to "turn off" the 505, you don't actually turn it off. What you do is put it in sleep mode. Sleep mode still uses battery. In the advanced options is where you go to find the menu to actually turn off the power for those times when you will not be using the 505 for at least a few days.
If it really is the battery, I don't think the USB port will work to charge it as you need some amount of power. What you can do is go out and get a PSP AC adapter that has the barrel type plug to charge the 505. You can turn on and use the 505 while it is charging via the AC adapter. You cannot use the 505 while it's charging via the USB. You can get a PSP AC adapter at most computer game shops.
Here is a PSP AC Adapter from Gamestop just to show you what it looks like.
http://www.gamestop.com/Catalog/Prod...oduct_id=37474