The A/C on my daily driver Lumina decided it didn't want to work this year. I got a recharge freon/oil can for it...per the can the system should have between 25 and 45psi on the low pressure side. It had about 15 psi, so I charged it up to about 40psi. The compressor still will not kick on. Is there something else I need to check?

you need to take the car to a Automotive AC shop.

Those are running pressures. The compressor has to be pumping freon to measure the 15 to 40 psi. If the compressor isn't running you probably need about 80 psi in the system, but you won't be able to get that from one of those refill cans. You have a leak so that needs to be fixed before you pour your money down the drain buying freon.