Need help please 2000 FRC won't start but battery is good
 

I am having some technical issues I think but not sure where to look. This past Monday it was pouring down rain and I drove about 5 miles to the store and back for gas. Didn't drive through any high water anywhere but I went out to start my car and it was like the battery is dead or low but when I turn the key off I heard relay's clicking. I checked and #37 (monitor ld) and another one across on the other side I think 42 but same type repay in fuse panel in passenger floor board. So I was able to jump start it from another vehicle after running it to help charge the c5 battery and it was real sluggish and sounded like it wasn't gonnna start but finally did. So I drove it around to charge battery was charging at 13.5 or so on gauge and then when I got back I turned it off and checked it to see and it wouldn't start doing the same thing. So I've been charging the battery for a day but still does same thing and battery reads 12 volts with my meter. Any suggestions would be greatly appreciated. And I checked and all the lights even hood light are shutting off.
Thanks

Not much of a c5 guy,but it sure sounds like a bad battery to me. A normal charge level is over 14 volts either from the car's alternator or a battery charger. A good hot battery will read well over 13 volts,maybe up to 13.8 with no charger on it for several hours. A 12 volt battery is pretty low when it reads just 12 volts. How about your meter? Are you pretty sure of it's accuracy? You could also have a starter that is dragging,from worn bushings. The combination is deadly,a marginal battery and a dragging starter,get out the tenny runners 'cuz you ain't gonna be driving! About the only way to tell(on either) is substitution. It's a lot easier to switch a battery than a starter!
Ron