PSP Sees to be charging, but won't stay on.

What ansfarid is trying to say is that with a problem like this the first thing to try is a firmware update, you can do this online with your PSP or with a very recent game, this can be a problem if you are using a "home-brew" firmware or if indeed the latest firmware is the problem.
However it sounds more likely that either your UMD drive or battery contacts or possibly both need cleaning. The PSP will crash out on disk read errors so try cleaning the drive and your disks first, even if they look completely clean.
You can clean the laser of your UMD drive with an alcohol-free CD wipe wrapped around a cotton bud (q-tip) but the most effective way is to blow it out with an air duster (available from any hardware or good electronics supply store).
Cleaning UMD's is a different matter, it is possible to tern the centre of the disk with one finger whilst holding an alcohol-free CD wipe to the disk surface with another but you can also purchase UMD cleaning tools from most large game retailers that make the job a lot easier.
cleaning the battery contacts is much more straightforward, just remove the battery and use a lint free cloth or our old friend the alcohol-free CD wipe to clean the contacts both on the battery and in the PSP, if you use a CD wipe make sure all contacts are dry before re-seating the battery.
As always message back if non of this helps or you need any further advice.

Change your battery

You better try your PSP by upgrading the software because there may be some errors had occured in your PSP OS software.