Air Conditioning - Central A/C doesn't turn on

Hello, experts,
I live in Houston and have 2 units (10years old) in my house. 1 for downstairs and another for upstairs. The one for upstairs doesn't turn on. I mean no single part turns on (including vent blower and outside condenser) when I rotate the dial of thermostat no matter what state (heat or cool) I set it to. I do hear a click (like the normal sound when the system was OK) when I rotate the dial. I guess the thermostat is gone. However, it's a purely analog (mechanical) thermostat that usually fails eventually rather than stops working suddenly.
I checked the power for the out unit and it shew 240V. I switched the breaker back and forth without success. Any comments are warmly welcome.

Check for 24 vac coming from the transformer. Also if your air handler is in the attic check the secondary drain pan to be sure that water isn't in there and shut it down via a safety switch.

Thanks a lot for your reply. I'm a green hand on HVAC but with EE knowledge and experience. Please tell me how to "Check for 24 vac coming from the transformer". I mean where I can probe. I checked drain pan and found it's as dry as Arizona. BTW, my units are from Carrier and no manual in hand since I bought the house used. Any reading recommendation? Thank you.

There are several ways to check but you can check at the secondary of the transformer or you can check at the sub-base of the t-stat. R to C and if you read 24 volts at your t-stat and not at the coil of the contactor your t-stat is bad. Have you checked the t-stat wires going to the condenser? Weed eaters can cut or fray the wire and then you won't have voltage (24 volts) and you could also damage the transformer. Check for a fuse either on the circuit board or in-line with the secondary of the transformer

Take the door off the units . Most of the time there should be a wire schematic on them . This will show you where you can check the 24V out. Need a cheap meter for this. If you jump R to G at the tstat base you should get inside blower that can tell you if its the tstat.

Thanks again for the replies. I checked nodes labeled G (green wired) and Rc (red wired) and some other nodes at t-stat base and there was no voltage in between any of them. I opened the outer unit and found the the wires hooking the power relay are red and white. I also measured all of the red wired nodes vs white wired nodes and got 0V. Meanwhile I applied the same measurement to the t-stat of the working unit and that gave me 270-290mv (may not be accurate since the battery is running out). At this point, I guess the 24V transformer is the problem. But my following questions are, 1) Does each unit have its own transformer, otherwise it can't be explained why one works the other doesn't; 2) where is the transformer located? I searched around but didn't find any clue. Thank you.

Each unit will have its own transformer located in the airhandler.

Thank you all for your info. I finally found out the problem was a loose connection and fixed it. Now I can sit in the chill and type this post. Thanks a lot.