just take it to a shop and let them do an actual AC job and tell you what's wrong.
There are many do it yourself jobs, but AC is one of the ones you dont really want to mess with because it can cost more in the long run
You should have a fuse and a relay for the compressor. Verify both are good. Next step is make sure your HVAC system has power. Next step turn your ac itself on and check to see if the ac compressor is actually spinning and not sitting still. If it is not kicking it it means it either doesn't have power OR a pressure switch (low or high) is keeping the compressor from running in order to protect it. at that point get your gauges or someone with gauges that knows how to open a system up and check the pressures
Note: the Walmart brand R134a instructions are not right. It said to fill it to 40 psi at 90 degrees ambient temperature, (or something like that, don’t remember the actual numbers) but I had to put in like 30 oz to get close. Turns out the total capacity is wall less than what I put in, and it wasn’t empty to start with. I would suggest taking it to a shop, letting them suck everything out, and then put the right amount in starting with nothing. If you do what I did, you end up having to take it to a shop anyway, and spending more money than if you had just taken it in in the first place. I just made this mistake last week, it ends up eating money. Unless you know it’s all the way empty, I would suggest not adding any refrigerant. If it is empty, add one with a tracer dye in it so that you can use a black light to find the leak. Then once you get the leak repaired, you can refill it to the proper capacity. If there isn’t a leak, and it’s already full, you probably have an issue either with electrical or the clutch/compressor is out. Does the fan turn on at all?
if nothing turns on, I’d suggest testing the switch. If the fan turns on, but not the compressor, and it can switch between zones, it’s probably not the switch or vacuum lines. But any test that costs money would probably be better to leave to a shop. Most AC things require EPA certs and I just learned that if you overcharge your system, letting the excess out in the air is a federal offense. If I can figure it out, I’ll post a link to my thread, it had some helpful info in there from other people just regarding AC systems in general.