I have the carrier programmable touch-n-go thermostat. It was working last night but when I woke up this morning, there is nothing but a blank screen on the thermostat display. I tried changing the batteries and checking the breakers but nothing has worked.

SOURCE: Carrier Comfort 13 Puron model 24ACA3 / FV4NB006

Verify 24 volts at the low voltage transformer inside the air handler. If it is OK, jump out the red/green and yellow thermostat wires. If everything comes on, replace the thermostat.

SOURCE: my programmable "Carrier"

blown fuse on circuit board, or transformer dead, or hot (red) wire disconnected or broken somewhere in circuit.

SOURCE: Carrier programmable thermostat

if it takes batterys pop some in and see if not it gets the power from the indoor unit

SOURCE: carrier infinity a/c thermostat screens are blank - no power

There is a fuse in the control panel, and depending how they wired it may be a inline fuse. also there is a fuse in the airhandler also they both should be a 5 amp auto fuse.

SOURCE: My AC stopped working last

There are quite a few things it could be, if you out door coils are dirty then it could have tripped the High pressure switch, some are manual and some are auto reset but you may have to cycle the thermostat to reset the lock out relay. If the coil was dirty this is normal, you should be able to see thru the fins, use a garden hose and nozzle use enough pressure or stream but don't damage the fins. A clean out door coil will make it as efficient as possible.
If the above failed, then it can get harder to advise you on the info that I have, if your indoor fan runs when it is calling for cooling, then the out door unit Heat Pump or A/C condensor should be running as well, as long as there is power. More unit information would help, if the above does not work.
Good call on the capacitor, the goo is supposed to be inside the cap.