Jamie, thanks for clarification.
I assumed since OP was talking about a dead chassis battery that couldn't start engine, even with generator running, that you used the solar on a disconnected chassis battery. My bad -- you know what they say about assumptions.
It does sound like you have a house battery on its last leg. By the way, does your solar charger indicate power level, or some other feedback to confirm it's working?
I guess we shouldn't expect much from 6 watts (likely its rating under ideal conditions). That's only +/- 0.5 Amp, which means maybe 2 Amp-hours per day. In a month that would be maybe 60 Amp-hours, or less than a bad battery runs down (i.e. -- a poor battery often goes dead in a month). A higher-capacity solar system may do the trick though.
__________________
|