My car's wipers seem to want to turn in the wrong direction!

Background - had an alternator failure on the motorway earlier in the week. As the battery finally died the windscreen wipers came on (I couldn't stop them), eventually stopping in a near vertical position. Local garage replaced the alternator, but the evening after picking the car up I discovered the wipers weren't working. Initially I thought it may have been a fuse, but having played around a little bit they seem to be getting some sort of power but want to turn down into the engine bay. I've tried moving them to the vertical position and that doesn't seem to help (very little to no movement there).

Thoughts? Google suggests a mechanism issue - what's the easiest way to narrow it down to this? I'll take it to the garage on Monday when they're next open, but if it's a quick fix I'd quite like to do it myself!