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2005 C6 throw up random warning, service soon, shocks inoperative, low fuel, service anti-lock brakes, abs light will come on. And somtimes it will go away, and come back.
Check the battery voltage but also remove the cables from the battery terminals and clean them really good. In *my* experience, the battery has always shown good when things like this happened but checking the cables at the terminals always showed them less than shiny. Cleaning them really good to a high luster always got the car working properly again since the battery was indeed fully charged and providing the necessary voltage.
Plenty of threads on how to track down good and bad connections from the battery to the alternator, starter, etc. Seems to me most of it was just dirt and corrosion rather than actually bad components. Indeed many times I had my battery on a Battery Tender to keep it "topped off" but I still had issues until I cleaned the cables and terminals really well and the car came right back to life. Try that first as it's a quick and easy check/fix.
You need to get more familiar with the abundant source of info on this site. The problem you have is posted maybe three times every week. 98% battery issue. Do a search for more info.