Hi Mark,
Yes, it seems you need a new pair of house batteries. If the battery voltage drops quickly from 11.7 volts while trying to start, they are surely dead.
When replacing your batteries, I advise to consider a pair of 6V AGM batteries. I found the 6Vs work much better together than 12Vs do. Because 6V batteries are taller than 12V, I had an interference problem in my 2007 battery compartment. So I replaced the raised battery tray with a flat stock metal bottom and bought a pair of maintenance free 6V AGM batteries. I installed them in 2015 and they remain there today in great shape.
CLICK HERE for my write-up on changing to 6V AGM batteries.
CLICK HERE for pictures of my battery compartment splash shield to protect them from tire splash. I am not sure if your 2008 PC model 2900 has the same condition as my 2007 model 2350.
A battery tray is an absolute requirement to maintain acid levels. So if going with wet acid 6Vs. you will need to replace your battery compartment frame with a taller one that hangs down lower. I think Phoenix has them available. Keep in-mind that doing so, the battery frame will hang below your battery compartment door by 2 extra inches, a simple cosmetic issue alone.
Whether 6V wet acid or 6V AGM, going from two 12V to two 6V batteries will greatly improve your power reserves for your house when camping for multiple days without shore power, and two 6V batteries live twice as long as two 12V batteries with less acid boil-over messes to deal with all the time. AGMs simply don't boil over. They stay clean, clean terminals, acid-free, and maintenance free. I went through two pairs of wet acid 12V batteries that provided us with only two good years of service each. One of my best improvements made to our PC was going to two 6V AGM batteries. Six years so far and all is well.
I have to add that converting out our florescent and incandescent lighting to LEDs also helped with our battery reserves.
CLICK HERE to read all about it.