Welcome to the thread and thanks for sharing the experience.
You never know how you'll be repaid for your help at a Heath/Zenith store! If all the parts are there, you should be able to finish that gem of a wx station. Just be patient and do a good job.
The only thing I can think of is the electrolytic capacitors may have aged, but they were all standard. The only weird things were the beautiful blue display, and the custom chips to run the thing. I don't see how the chips would be bad.
Another Kevin here is also a very accomplished 5001 fan, and may be a source of information in case you get hung up, but a lot of people built these (or at least those who could afford them at the time), so I'm sure another one will be up and running soon. Note that there are the humidity sensor units available yet, as mentioned here.
As far as the manual is concerned, is it a bound book, or a loose leaf three ring binder? It wouldn't be too hard (just time consuming) to scan that baby into a pdf, perhaps a chapter at a time. The mechanics of it would be lessened if it were a loose leaf, since I think many multifunction printers/scanners/faxers have a very good document feed system that might lessen the hands-on time. If the book is bound, then each page would have to be turned and placed on the scanning device. Been there, and it isn't a fun job even with good music and something to drink along side for the experience.
Keep us posted. Any chance you could scan and attach or photo and attach the table of contents to that Blue Book?
Dale
K9ELD