nut on linkage may be loose
If the windshield wipers don't move but you can hear the motor running, it may be the nut on the linkage is loose. I believe this is by design to keep the motor from burning up or the linkage from breaking. Unfortunately, this nut is a bear to get to. Open the hood, remove the plastic cowling up by the wipers. If you have small hands you can reach in and feel the nut that attaches the short link from the end of the motor to the windshield linkage. See if it is loose, if so this is the problem. It also may have fallen off but hopefully is still in the cavity. So, turn the windshield wipers on and then off to make sure you are in the parked position, by hand move the wipers to the parked position. Now we will tighten the nut. You will need a 14mm wrench ( I used a 1/2" and it worked ). Luckily, I had a nice Craftsman ratcheting flat wrench. Very difficult to get it in there but it is possible. Tighten the nut, I believe it just holds the linkages together with friction (maybe a couple dimples ). I would not loctite since this is the weak link, meant to loosen when the wipers are frozen to the windshield. Hope this helps, I have done it twice, really is a bad design. My Toyota just does a similar thing but on the wiper so tightening it is simple.