Is there a way to unbrick a PSP?

I got two PSP games for Christmas. After I put one of the game cartridges in the game slot, the screen said I needed to update the software. I scrolled through all the screens I needed to get to the point it started downloading the upgrade. As it was doing this, the screen went off but not the power. Figuring it was going to take a few minutes to download, I left the system alone for about five minutes. When I came back to it and tried to turn the system back on, it wouldn't do anything. Only the green "power" light would come on. My brother said I "bricked" the system. Is there any way I can fix unbrick my PSP? The warranty is expired since my system is over three years old and it's going to be a week or two before I can afford a new one. I have the original PSP, not the 3000 or Go.

Anything else you need to know, feel free to ask. Thank you in advance.