NEVER run your furnace with the front panel removed. Are you talking about the upper cover that covers the gas valve, burners etc., or the cover for the blower/filter compartment? If it is the lower access door for the blower compartment, the furnace can and will draw in combustion gases and send them into the house which
can cause health problems or even death.
If you are talking about the other door, this wont happen however you should not
run the furnace with any doors missing.
The furnace has a "Door Switch" that is designed to prevent the furnace from operating if the door is not fastened correctly. If replacing the upper door is causing the furnace to stop running, it may be somehow interfering with the door switch causing it to disable the furnace.
Locate the door switch and observe it while installing the upper door, does it cause some deformation when installed, or does it cause the lower door to not seal properly? In some applications the upper door must be installed before the lower door and visa versa in some furnaces.
This door switch is most likely the source of your problem, however the upper door may be in contact with some furnace wiring when installed. You need to observe these things when installing the door and you should be able to determine exactly what is causing the furnace not to operate.