you will need to get a new AWC after your all done with repairs but the old one would be good document to have,..I'd get all of the paper work available first ,..then go from there,..I'm sure from what you have said about the planes condition that the present owners have not kept the paper work in order as well,..if your missing anything ,..you should ask the owners which office they used when they first did all the paper work ,..contact them for missing documents ,..they have an archive and should be able to get you what you need ,..just saves allot of guess work knowing which office was used. if it was actually registered.
Your basically going to have to look at this as a new first time rigistration ,..it might be required that you do a new phase 1,...especially if major reconstruction is involved,..any original phase 1 documents,..a big plus if available,..the original pilots log book if an airframe log book isn't available,. should have this and possibly a copy could be aquired of the times and fly test's done,..have you got the serial number from the present owner? you can do a quick back ground check on the serial number or tail number if it was previously registered.
I recently helped someone on the forum that had similar issues ,.. he has got it all in order now,..even though allot is said about the FAA in a negative way,..the offices are more then willing to help with previous owned/registered aircraft to get all in order concerning documentation ..it also makes their jobs easier getting it right.

Chase