The problem with the gauge & can you bought from the store is that its only reading the low pressure side of the A/C, and you need to measure the high pressure to know if the system is working.
There should be both a low pressure and a high pressure cutoff switch in the system. If the system is contaminated (and something maybe plugged), the high pressure cutoff may prevent the system from coming on. On the other hand, the low pressure cutoff will disengage the compressor if there isn't enough R134 in the system.
I think most places charge too much for a basic A/C service, since they just let the machine do everything to evacuate and recharge, but you might have to pay for the service just to get started on troubleshooting. If basic evacuation and recharge does not work, then you have to hope they can narrow down the problem to something you can fix (relay, temp sensor, orifice tube, etc.). If you have to open the system you will want to replace the receiver/dryer, and maybe even have it flushed.
Bruce