My tenant is trying to turn the furnace on for the first time this fall. She can get the blower to blow out cold air, but not hot.

I told her to turn the (digital) thermostat to "off" and to leave it off for a bit. Then to turn it to "heat". She says when she does that it just blows out cold air. She has also tried it on "auto" with no success.

Oh, yes, she also said there appears to be a red light blinking on the back of the unit.

Any ideas, suggestions to try, anything?

You can count the number of blinks and look at the legend inside the blower door panel for a diagram with what the blinks mean. It will give you a ruff idea of the problem.