READ WHOLE REPLY FIRST!!!!
you would have to find out the model of your motherboard. If it is TA-088v3 which is the most common of all the 2001 models then it is unhackable so far as ive heard. to find out what your motherboards model is you have to open your psp and find some writing on the board that says TA-0-- and whatever those last 2 numbers are is your model. but as to which version of that model it is i couldnt say for sure...
but before you start serching the internet for info. look up a tut on youtube on how to open a psp 2000. and once you have it open and have the screen removed look for that writing on the motherboard. and tell me what it is. (dont open your psp if your extremely nervous about doing it, chances are you will ruin it then)
if you really want to mod your psp to CFW you need to know the model... but if you just want to run homebrew you need OFW (Sony's firmware) version 6.00 or lower to run HEN (if you dont know what hen is then look it up on google) then you dont have to open your psp.