If you own an old PSP, and are a little teary at the prospect of missing out on all the Skype fun PSP-2000 owners will be getting in on, sorry. Nothing's going to help you. Your "ancient" device just can't do it. Apparently. Hopefully the knowledge of why you can't get in on the action will help you in the mourning process. SCEE's Nick Sharples explains:

Although PSP-1000 and PSP-2000 are identical in basic functions, there are differences in hardware specifications to some extent and for that reason, PSP-2000 may differ in features from PSP-1000. We had studied the possibility of supporting Skype with PSP-1000 but had to give it up because of the smaller size of main memory on PSP-1000 series.

There you have it. Don't blame your PSP's girth, that's shallow. Blame its smaller memory. Then blame Sony, because even if that's the truth (and we have our doubts, what with this being a great "incentive" for people to upgrade), if you're an early adopter this kinda sucks.
PSP memory was key factor for Skype decision [Pocketgamer]