Thank you for the replies!
We're going to bring it to an MB dealer/service shop next week.
The hard top doesn't latch completely in the front, and the alarm dings. When we take the top off, dinging stops.
But soft top won't close either now! It did when my husband tested it. Now the top raises, but the boot won't close. Seller says when they tried to manually close it they "reset" the memory or something.
We'll see what happens at the MB shop. We got it for a great price, and the body and engine seem to be in excellent condition. So even if the top repairs cost a couple of thousand I'll be OK with that. If it's a lot more, ouch!