A/C works intermittently

I took my vehicle listed above to a local Chevrolet dealer for a recall and when I got it back the A/C only works intermittently. Of course, I took it back to them five different times. They vacuumed the system and recharged it three times, inserted dye to find the leak they were sure we had. They found no leaks. I was getting pretty frustrated and took it back one last time. They called after 3 days and told me this: "there is a relay in the fuse box that is built in that controls the compressor. It should have a spec of 1 Ohm and it is reading 108kOhms. It is tripping the compressor on and off. This vehicle needs a new fuse block. The total out the door would be $480.00".

I would like to not give them that kind of money to repair something that was working when I dropped it off to them. Which fuse block is this relay located in? Is this something that a novice but fairly mechanically inclined individual can replace?

Thank you,
Jay