On Tue, 10 Dec 2013 13:43:19 -0500, David L. Martel wrote:

You're testing the wrong things. The thermostat is very unlikely to fail.
Please put the thermostat back together. Now slide the fan button to "on".
Does the fan come on? This will tell you whether there is electricity going
to the furnace (?). What sort of heater are we talking about?

I don't know anything about heating systems; so, I was planning on debugging
from the thermostat to the furnace.

The furnace is a Payne 394JAW, built in 1988.

I called Carrier this morning (800-227-7437x4) and asked for a troubleshooting
guide and parts list. They said I had to go to a local dealer, but, they did
send me a document named: 40394dp65-a.pdf, and titled:
Bryant, day night, Payne 394J, Series B, Sizes 030 thru 095, 40394DP6-A 10/15/87
installation, operation, and maintenance instructions
Upflow Gas-Fired, Natural-Draft Furnace, 9 pages
For use in California only
Cancels 40394DP61-A

BTW, where can I post this PDF so you (and others) can see it, as I couldn't
find anything on the web for how to troubleshoot the furnace itself, and the
four companies that Carrier told me to call all told me to take a hike (in
effect). They don't deal with residential consumers, at least not for PDFs
and parts orders.

NOTE: I'll see if I can convert the PDF to JPG so I can post it for you...