It depends on where you live, but yeah sony still repairs PS3, PS4, PSVITA, PSP and PSPGO systems. however, their policy is to do a memory wipe before servicing your system, so you'll want to find a way to backup your stuff, if you can still turn your PSPGO on, before sending it in.
Here in my country it's about 69.99 - 79.99. It's definitely cheaper than buying a new one, but you'll have to get on the phone with sony customer service for them to send ya a box, so the whole process can be authorized, etc.
EDIT: It's a bot, fucking hell