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.
Could be a RAM issue. On this model I believe that there is one stick on the bottom and one underneath the keyboard. Try removing one at a time to see if either might be causing the problem.
Try wiping the connections on the screen cable with a Q-tip and then reseating it. If that doesn't work then it sounds like you got a defecting replacement screen.
This part scared me, never in an iFixIt guide have I seen a warning like "trying times are ahead".
I used a plastic iPod opening tool and ran it around the seam in the same order pictured. I had the plastic off in less than a minute with almost no fuss.
Unlike the DS Lite and later models, there is no reason to take apart the bottom portion of the original DS in order to remove the top screen. The first ten steps of this guide could be skipped.
This part scared me, never in an iFixIt guide have I seen a warning like "trying times are ahead".
I used a plastic iPod opening tool and ran it around the seam in the same order pictured. I had the plastic off in less than a minute with almost no fuss.
Unlike the DS Lite and later models, there is no reason to take apart the bottom portion of the original DS in order to remove the top screen. The first ten steps of this guide could be skipped.