Hi Mike, it sounds like there is an issue with the ribbon cable? If that is the case, you should just order the part from eBay or a wholesaler and if you are comfortable enough I would say go for the soldering. Just remember it is a different thing soldering on computers vs micro boards like phones.
There could be a few problems. First, there can be a software problem that can usually be solved through a restore or an update. Second, if you ever had any kind of repair on your phone by a third patrty, there usually is a problem with grounding. There are multiple points on the iPhone that help it stay grounded. All screws and parts are there for the phone to function like it was intended. However, if these parts are neglected, the phone will have issues.
You definitely need some soldering experience but the repairability is not that difficult. The soldering points are big enough for any cheap ($40) soldering iron can get too. As for removing them, it helps to use flux and also a soldering wick to absorb all the old solder. It is not easy but not the most difficult repair. P.S you do not need the expensive soldering stating with hot air etcetera. This works perfectly as it get hot beyond the required point to melt the solder
Mick, the camera you got with your new screen should work. But since obviously it's not I'd suggest to transfer the old one. Very simple and won't take too long!