two things:
1. your tv may be using more power than you think. 100w sounds too small.
2. and your cig lighter outlet may be limiting enough power to run the inverter at the full 100w.
you need to determine what the 12v outlet is rated at.
try hooking the inverter right to the battery and see if the same thing happens. my guess is the 12v outlet is the issue.
i just hard-wired my 400w inverter straight to the batteries, so there's virtually no battery power loss. my Roo didn't come with a 12v cig lighter outlet.
you might want to ask someone on the Hybrid Forum, that has the same Roo as you do, to see if they have any similar problems.