A couple of thoughts on your issues.
A) as others have said your battery is toast.
B) Tripp Lite will not charge a battery that is that low, so that could be why your it does not appear to be working. There are LED's you can check. Attached the manual.
C) The AC should pass through the Tripp - lite, there are some breaker resets on it also.
D) You most likely have Sure-Power Separator, based on it being a 2006. That would also explain the click when you started the Van, it was the Sure Power Relay closing. I would try starting and running the van again, it may be on the second restart you did not wait long enough for the van battery system to reach the correct voltage to engage the Sure Power.
E) You will need to have power to the GFI outlet to reset it.
F) Also you mentioned that you were plugged into a GFI outlet. Make sure that you did not rest that outlet.
http://www.sportsmobileforum.com/vie...hp?f=14&t=8212
Attache Tripp-Lite manual