If you’ve had your PSP repaired, either officially or unofficially, chances are, parts have been swapped and a particularly obscure difference introduced that will render your PSP’s ability to use Remote Play with your PS3 broken.
For Remote Play to work, it is important the Wifi MAC address is correct, as this is what is used to associate the pairing. Because of the repair, the MAC address the OS thinks it has may now be different from the actual MAC address of the Wifi chip, so remote play will no longer work as the pairing between the PSP and PS3 will be considered invalid – and even making a new pairing won’t work, as the PSP will report the wrong MAC address to the PS3.
If you are running custom firmware, you can use this tool to reflash the OS to report the correct MAC address automatically: http://www.noobz.eu/joomla/component/option,com_remository/Itemid,0/func,startdown/id,24/
If you’re on official firmware then unfortunately you’re out of luck until you can get it reflashed with custom firmware.