2000 GT intermittinly fails to start, any help would be awesome?

"Aftermarket alarm" is the first red flag I see. Try disabling (unplug completely) it and see if anything changes.

The problem is, aftermarket alarms are notorious for not integrating well with PATS, which is the factory installed anti-theft system.

When you experience the no-start issue, does the little red 'theft' light in the cluster flash rapidly? If yes, that is an indication of PATS being activated.

I will try that, but doesn't the alarm have to be connected to allow the starter relay to energize in turn allowing the engine to start? I do not know what the PATS is but I do know when the aftermarket alarm was installed part of the factory alarm was removed. Thanks for the info. Any thing else will be appreciated.

starter relay is under hood in fuse box. 1"x1" swap them around and try it,(thay are all the same) . . you cannot just unhook the aftermarket alarm , you have to completely remove it from the car and repair all wires used for it . most systems cut in the starter and ignition wires to operate it , some go into the window wires also, so you will have to reconnect them togather