Did the monitor come with a three wire AC power connector like this?
Most contemporary monitors use this kind of three wire connector and an AC power cord with the appropriate plug for the region (U.S., Europe, etc.). The middle connector is chassis ground. The other two are hot and common.
If that's what your monitor had, and you want to solder the AC wires directly to the circuit board, you need to know which of the remaining wires is hot and which is common. A better solution would be to find an electromechanical replacement AC receptical and solder it back into the circuit board. That will automatically keep everything polarized the way it was intended.
These sockets should be inexpensive (a couple of bucks) and not hard to find at any electronic parts store. Assuming it's PC mounted, you want to ask for an EIC AC receptical. The most common difference between the ones you'll find is whether they're straight or right angle mounted.