These units, while hot swappable, will NOT
start with dead batteries connected.
You will have to replace the batteries to confirm if the unit is still usable. Sealed Lead Acid Batteries do have a shelf life when a charge is not applied and will fail after several months of sitting around.
If your unit was working fine before it was put in storage, I definitely would consider just replacing the batteries. It is possible that the batteries are connected loosely, you can try opening the unit up to double check all the connections but if it has been sitting for more than a couple months, I would definitely consider the batteries dead.
You can find replacement batteries here http://www.refurbups.com/Tripplite-SMART2200RMXL2U-Batteries