I think the table above is a bit old - the TA088v3 is no longer "unhackable" according to these guides:
The question is - is yours a TA-088v3. Sounds like it could be. Google a few more of those "how to tell the motherboard of the psp" guides to see if you can get a more definitive answer.
(I think) PSident will be of little use to you because you need to hack the psp in the first place in order to run it!! (I think)
By the way - it is actually possible to run emulators etc on the psp without hacking it at all. If you search the internet hard enough, you might be able to find "signed" versions of emulators for psp. These would run on official firmwares but they may be hard to find and not all emulators might have been ported