You need to fix ( or disable ) the key in ignition switch as the alarm might be looking at that to operate / arm.

Does the square key have a very short head? If so it is called a "flat key" ( wallet key ) and should work in all locks ( if they have not been changed )

The round key is a "valet" key designed for door and ignition operation. ( Not sure if it will open the passenger door.)

Take a look at the two key profiles, the square / flat key will have a extra groove on the edge where the valet key won't. This is the mechanism that keeps the valet key out of the glove box / trunk.