There's a hack for the PSP known as the "Pandora Battery". I was the definitive solution until some later model PSP-2000 units, and the latest PSP-3000 model. These were recently hacked using an exploit in the 5.03 firmware version.
However, you have a PSP-1000, so none of this matters to you. All PSP-1000s (The fat PSP), can be hacked using the Pandora Battery trick. Basically, you purchase a special battery which once insert, allows your PSP to boot from a special developer mode. This mode bypasses the firmware currently installed on the PSP, and instead boots off of your memory stick. From there, it's trivial to install any version of firmware you want, including custom ones.
For further instructions, please search Google for guides on using the "Pandora Battery", they shouldn't be hard to find.
Now, before you start complaining about having to buy some piece of hardware, the Pandora Battery costs less than US$7 from Dealextreme.com.
http://dealextreme.com/details.dx/sku.12472 If you want a Pandora Battery which you can use as a regular PSP battery afterwards, then that's lessthan $10.
http://dealextreme.com/details.dx/sku.15153 Hope that helps clear things up.