Had this same issue after replacing the front assembly. Reseated all the connections, reset the phone several time to no avail. Then I try popping the SIM card out and putting it back in (with the phone on) and suddenly it gets signal.
I've not seen this issue on the 3DS yet, but on the DS Lite sometimes the cable to the top LCD could be loose and result in the behavior you described. As someone else said it could be short (i.e. a broken cable) but I think it's more likely just loose. Check where the cable plugs into the motherboard.
Using quite a bit of force I've been able to transition from the top/bottom to one of the sides without removing the tool, just be forcing it around the corner of the device. It will mangle the tool, but they're meant to be disposable.
The best you could do would be to take it apart and see if you could clean that area. I would recommend a brush or q-tip with rubbing alcohol. In order to open the controller you need a security tox screwdriver, you can get them off of eBay for a decent price.
All of the parts that would commonly be replaced, that is the LCD, disc drive, and joystick are all interchangeable between any 2000 series PSP, at least in my experience working on at least a couple dozen of them. I would be surprised if anything else was incompatible. Besides, I'm fairly certain that the wifi chip is incorporated into the motherboard itself, making this a non-issue.