The furnace will light and run normally for 3 minutes then shut off, will try to relight but shuts right off, filters have been cleaned, limit switches and t/stat were temporarily bypassed but had no change on the operation, still shuts off.

Have you checked the relays in the system and the contact tips if it has them. Sometimes a coil will work when cold but overheats when in use (under load) because it gets too hot and loses its field.