This might be a long-shot, but I would also check the wire to the negative battery lead.
I had a 1996 (since new) that had starter issues around the 110k mile mark. The solenoid would click just one time, but the engine wouldn't turn over. I replaced the starter, and all was fine. A year or so later, I had the same issue...replaced the starter again, and all was fine. A year later...you get the picture. This continued to happen over the course of 4-5 years.
The 3rd time the starter went out, I was in a parking lot miles from home. Thankfully, I was able to tap it with a wrench to get it going again. When I got it home, I removed the starter and took it to the auto parts store for yet another warranty exchange. They tested the starter and told me that it was perfectly fine, but I assured them that it was not functioning when I used it. They then gave me a new starter, I installed it, and all was good again.
The 4th time, I wasn't so lucky. This time, I had no other choice but to change the starter out in the parking lot where my Explorer had left me stranded. New starter installed, went to start it up, and...click. She didn't start (and it was getting dark on that cold fall evening).
I had some electrical cables that I used to connect my winch (when mounted on the 2" receiver hitch) to the battery. Just to try it, I connected one of those wires between the starter and the battery's negative cable...it fired right up.
My negative starter wire didn't look that bad on the outside, but upon further inspection, it was heavily oxidized. It's worth looking into, though...unhook the leads and check the contacts for corrosion and such. Check the wire itself as best you can. If anything, at least you'll be able to rule it out and be more sure that your starter is actually the issue. I thought the same thing as someone else who posted...it can't be the wire if I could tap it to get it working...but it was the wire after all. Not sure if this was the "proper" way to fix it, but I got it to work...that's all I was concerned with at the time. As always, though...your mileage may vary.