Well it wouldn't hurt to just email them and ask if they still do repairs, I honestly don't think that they would keep that repair page up though if they didn't do it anymore.
I'm not sure how much it would cost to get it repaired, but there is a place that should be able to repair it. Check the second link for the info about the Sega CD model 1.
http://oldschoolgamer.ca/
http://oldschoolgamer.ca/node/144
Gary Shandling
I pasted three helpful videos below, the first is the door timing issue:
http://www.youtube.com/watch?v=ddGTV...eature=related
http://www.youtube.com/watch?v=6ap4o-ehz0M
http://www.youtube.com/watch?v=UFb21...eature=related