This could be one for the books!
As suggested by an earlier reply, we (my husband, Dick) reversed the hot and cold supply lines this afternoon. The hot water continued to work fine although it was on the opposite side of the faucet - turning the faucet to the right to get cold, now got hot. So, he decided it had to be in the supply line somewhere. He reamed out the new supply line he had installed (when he did the new faucet). No problem. Then he connected the supply line to the cold water line and tried running it into a bucket. It was very weak - not what it had been once before. Checked the new supply line again. No problem. Took a wire and put it down into the cold water pipe coming up from the supply line. Nothing at first but then he heard a clunking noise as the water ran for a few seconds and then stopped. Fished around again and then put into a bucket again. Out popped a small set screw!!! (It was about 1/2 inches in length with about a 1/4 inch head) What I did not mention earlier, as I did not think it important, was that the reason we were getting a new faucet was because we had just had our counter and sink replaced. The cold water pipe comes straight up toward the sink from the valve. We can only guess that somehow, when the company was removing the old counter and sink that one of the sink set screws fell into the open cold water pipe. It must have tumbled around for a few days the first time, finally settling into a position that blocked 95% of the cold water. When we were replacing the first faucet, trying to flush the line, banging on the pipes, etc., we must have dislodged the block and that is why the cold water suddenly came back - see first post that we did not know why it suddenly worked. After a few days, the screw must have settled back down into a blocking position. Apparently, the wire poking, along with the pressure from the line must have finally dislodged it enough that it was pushed out of the line.
Now, we assume that the screw must have inadvertanly dropped into the open cold water supply pipe when they were removing the old counter - a very difficult job - and sink. We had chosen not to pay the high price (so it seemed to us) to have their plumber install the new faucet. We saved many hundreds of dollars. The chance that this set screw would fall into the small opening of the cold water pipe seems almost 1 in a million. Thus, the one for the records title. The only other answer is that it was dropped deliberately by the counter people since we were not paying the extra cost for a plumber. We could not believe that they would really bring a plumber from such a long distance from their company just to install a simple faucet. Since we were not home when the installation was done we would never have know whether or not a plumber truly came. I want to believe in the best of people so will assume that it was a 1 in a million chance.
We now have wonderful cold water and our faucet is wonderful. We are very happy with this new style and hope that it will last many years. (It seemed strange about the bad Moen postings above - they did not appear to be legitimate answers.)
Thanks for everyone's advice. Trying the supply lines first to determine the source of the problem was great. Luckily, Dick, thought to probe the cold water pipe which had appeared to be working just fine. And, luckily, the water pressure was enough to push the screw out. My misgivings about his plumbing ability on easy jobs were wrong! Have a great week everyone. Sharon