Garage door stops at a different place each time it closes
Many times the most cost effective and time effective (and "time is money" cost effective) solution to strange problems with an old opener is a new opener.

You can, of course, replace parts; but you can quickly exceed the cost of a new opener, and parts often come with no guarantee, while a new opener generally has one. Since you KNOW your opener has been abused, that's another tick in the "reasons to just replace it" column. Recall that it is a device that can kill people if it malfunctions in certain ways.

I will also suggest (from experience) that you provide a surge suppressor on the outlet serving the opener.