Air Conditioner And Heat Not Working?

I noticed this morning that the heat hadn’t come on and it was set at 2 degrees higher than the actual temperature was. I didn’t think much of it at the time, but when I tried to turn on the air conditioner later this afternoon, nothing happened. No fan blowing inside for the heat and no fan blowing outside for the air conditioner. I noticed at the same time that the thermostat was acting weird, turning on an off by itself and changing settings if I tapped on it. I changed the batteries and it kept doing the same thing. A trip to Home Depot and an hour spent replacing the thermostat later, still no heat/air conditioning. The new thermostat seems to be operating properly (no flipping around or turning off by itself) and I’ve checked and rechecked the wires to make sure they’re clipped into the correct spot and all of the jumpers seem to be in place correctly. One thing that I did think was weird was when I took off the old thermostat, there was a very short black wire that had been clipped into both RH and RC but not into the wall. I didn’t clip that one into the new one because the instructions for the new thermostat didn’t mention it. My wires consist of W, Y, G, and RH and the thermostat manual doesn’t have any troubleshooting instructions in it. Before answering, consider that I’m a girl and my husband is out of town, so please talk in a language I can understand. I’m not an idiot (I did install a new thermostat by myself, thought maybe not correctly), but I need to be able to understand what to do, especially if it’s complicated. Thank you!!

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