ok there are a few ways you can go at it now
it maybe software but i am not sure but i am sure if we narrow or eliminate the hardware the circuits or components that power the psp software will be all that is left
you say when you push down to hold it stays on so lets start there when it cuts off there is no power light correct i ask to make sure it is not a backlight or screen issue
these steps seem a lot but what we are trying to do is narrow down the problem so we can do that my focusing of the section that powers your psp
all these steps must be done with care for if you miss one then we may miss the cause
1. open psp and i wouldn't bother checking switch but you can . I would buy another on ebay 6.00 dollars
2. while you have the psp open and the power board removed check here and here for brakes
old photo but shows power points trace from yellow [ac jack] the 2 wire to back also white block see if is loose
3.if no brakes or problems found wait for switch to arrive
you have already checked the battery prongs in rear and have tried a different battery right if not try this
http://www.psp-hacks.com/forums/f127...st1106893.html
4. we can also check the fuse while we wait a fuse is either go or bad but i have come across a few in my line of work that prove this to be wrong in some cases
5. reconnect your old power board remove lcd screen leave connected to mobo grab a meter and check here
see photo for location of fuse find a ground try the screw shown in photo and check both sides of fuse coming and leaving to see volts are steady if you have alligator clamps use those so your hands will be free so you can move around the wires and the points we checked above to see if we lose volts
if good switch meter to check continuity place on both sides of fuse and move fuse back and forth to see
if you lose continuity or volts [this is your problem] record the volts you get just for FYI
you could bridge fuse this is your problem or replace with surface mount fuse it is not recommended to bridge as a fuse is used to protected mobo but as long as you use a psp approved charger you should be good but the choice is your as well as the risk if you dont
6. if no problems found
when you receive new board install if problem still persist it is a software issue as we have just trouble shot the circuit involved in power you psp