Your bike is the same time frame (no pun intended) as mine. I have a 2005 Kuota with Campy 10 on it, Easton wheels. The issue you will run into is that anything new has moved on from those specs. The problem with shifters is that they are never compatible with anything else, Campy shifters won't work with a Shimano derailleur or vice versa, cassettes aren't compatible, wheels aren't compatible. All the systems have such tight tolerances that they only work as a group.
Here at Bikeforums though we are Kluge Central. My advice though is to stay away because once you get something to work you are then stuck with it because nothing else will, not even the compatible components. Somebody here will say to get a Shiftmate, that converts pull ratios from Shimano to Campy or vice versa. It'll work, maybe, but will it work well? Will you be able to swap wheels? Maybe, maybe not.
When I bought my Kuota new, I wanted Campy 10 but I had a pair of Velomax wheels that I liked that were Shimano. I asked if I could use a conversion cassette because everyone here said yes, but his answer was an emphatic NO. There just isn't enough room, and you are spending $3500 but you are going to use a kluge??? Just get fully compatible wheels, which I did.
The klugiest thing I did was to make a Campy spaced cassette out of a Shimano Ultegra. It works great but this is on my trainer, not on a wheel. While I could see how it could work I wouldn't want to be riding outdoors only to have the shifting be kind of funky. Indoors on the trainer doesn't matter. And to the shop's point above, the trainer takes 11 speed, which has more space than the 10sp that was available when I bought the bike and hence would work. But why would I build a bike with 10sp and then use an 11sp wheel? Just build it with 11sp.
And back to your specific question, you are unlikely to find a NOS ST-7800, but maybe you could if you keep checking. I just checked eBay and they were all used. A used one will possibly have the same problem as yours. Oh, and you are learning something else, Shimano can't be repaired, Campy can. I replaced the springs in my Chorus 10 and it shifts like new. If you buy a new groupset be prepared to buy new wheels too. Not sure the older Easton wheels can take 12 speed.
Here's a brief rundown of things that have changed in 16 years: 12speed, thru-axles, disc brakes, bottom brackets, seat posts, stems. In particular disc brakes, rim brakes seem to be disappearing from new bikes, and with disc brakes come thru axle hubs because they can take the braking action.