2000 Taurus won't go into gear.

It's very hard to tell without having been there in first person to see it. It could by anything from a bad computer to a clogged air filter. All sorts of things can cause running problems that you described. The cars computer controls the transmission so there's a good chance it's not the transmission at all.

This may sound stupid, but what would I have to do to find out. If I take it to a mechanic would he have to tear down the transmission or could he connect it to a computer to tell?

Somehow if you can replicate the problem while a mechanic is watching than you'd be in luck. There's all sorts of things that the real mechanics who know their stuff can do. My experience tells me that there won't be any engine codes unless you've seen the check engine light - light up at least once. Don't go to Firestone to check the codes. They charge $100 USD which is a rip off.

The best advice I can give you is either have a close friend who knows his stuff look at it and/or take it to a mechanic that is not the rip off dealership. Always get a second opinion before having some major expensive repair done.

Sometimes something as simple as a bad electrical connection or a $5 sensor can cause running problems. It can even bee a clogged air or fuel filter.

East-

Did you check the transmission fluid? It would probably not be the first time Quicky lube drained somebodys ATF. Most of the lube places do a good job, but it never hurts to have a look.