Aquatherm - thermostat is dead. What to check?
First off, check how many wires are connected in your stat. There should be 2. If so use a tester set to volts AC. Test for power, you should get 24ish volts across the two wires (usually .W and R or Rh). 

If you get 0 or 120 you have a different issue comment back and I'll edit the answer.

So 24v at the stat; jumper W and the R/Rh with a small peice of wire or unscrew them and twist together. If the heat comes on your stat is faulty.

Since you already have a Nest, no point in perusing a stat repair. Now you need a common wire if there are indeed only 2 wires you have an issue. You'll need to pull another wire. That's another ball of wax covered several times on the DIY stack exchange.

Try the steps outlined above. It will confirm the status of your thermostat.

EDIT

Disconnect the white wire and the red wire from the wall and twist them together. After a few minutes you should have heat. I don't know why there is a wire on the O terminal without a wire on the Y terminal (unless there is one hidden) do you have air conditioning? If so Nest will be tricky if not you can use the wire conectet to O for the common.