As others said and it’s my guess, that it’s icing up. You really need to get up there (even poking your head up in the attic) and listen to hear if it’s running. Turn your T-stat UP so it doesn’t call for AC and just tell it to turn the fan on. Then poke your head up there and see if you can hear it spinning. A bad cap will usually result in a sort of grinding/buzzing sound every few seconds until it times out, probably not the case.
It’s also probably not a bad t-stat since the compressor (outdoor) unit is coming on. I can go into detail, but, I’ll rule that out.
I also doubt it’s a blown fuse since it probably (but I won’t promise) be able to call for the compressor to turn on with 120v service to the air handler (furnace).
Assuming you can hear it running, it’s very likely iced up. You’ll want to find the root cause, scratch that, you’ll hope it’s due to a dirty filter*, so check the filter, if it’s dirty, change it. Someone up thread mentioned just leaving it off for 24 hours. That will let it thaw. A faster way is to let the fan (and the fan only) run for a while. The moving air will clear the ice much faster. Hour(s) instead of a day. Since this isn’t in the basement, you’ll probably want to keep an eye on the drain pan/tube. Both because if it’s iced up, you’ll see it draining and also because if it’s iced up you’ll be seeing a lot of water coming out and if the tube is clogged it’s going to over flow. Overflowing on a concrete basement floor isn’t that big of a deal, overflowing in the attic might be.
If you can get up there, you can check the code on the board by pulling off one or more access panels and looking for a blinking light (and a legend), though, off the top of my head, I’m not sure how much info it’ll give you for AC, it’s mostly designed for furnace switches/faults.
*Couple more things. If there is ice, it’s either a blockage (usually dirty filter or dirty evap coils) or you’re low on refrigerant. The filter is easy. The coils are harder. Low charge requires a pro.
electronbee mention that it could be a fan relay. That’s on the board and could require a new board. You might get away, if you have the option, of switching it to a different speed, but if you have a bad board, they can be pricey to swap out. Sometimes, enough that it’s worth (at least) getting quotes on a new unit. If you’re current one is old.
If it’s a bad cap, they’re very easy to swap, but take pictures before you remove it, especially if it’s a combined start/run cap, so you put all three wires in the same place. If you have the know-how, do that yourself. It’ll take 20 minutes and $30 or repair guy 20 minutes and $150.
As I re-read this thread that I realize is several days old, I see that you mentioned you can hear a click when you move the t-stat up and down. That’s good. It likely means the relay is working. But I’d still want to know if the blower comes on when you set it to fan-only, that’ll go a long way in troubleshooting the problem…short of you opening up the plenum (there’s usually an access hole) and checking for ice.
This is one of those things that difficult to diagnose over the internet. We can help you, but only with the information you give us. OTOH, I could be standing there with the case wide open and say 'look, this wire is totally burned up, there’s your problem. Or, while I’m comfortable just hooking a motor directly up to line voltage to rule it out, many people aren’t.
So, are you still having this problem? If you are:
1)have you checked the filter?
2)any thoughts on the ice situation?
3)Do you have a voltage detector and are you comfortable working with it?
In the end, as long as you have a full charge (difficult for a novice with no meters to tell, I know) and you’re comfortable poking around and replacing parts, you can probably fix this yourself, either something needs to be cleaned or replaced. Just cross your fingers that there isn’t a leak.
FTR, shadetree (and mostly commercial) HVAC is what I do on a regular basis, forgive me if I got any details wrong in the middle of the night trying to walk my way through this without a lot of info.