It sounds like your battery. Have you tried to warm up your battery before shocking it trying to turn the motor over? Warm it up by cutting on your headlights for about a minute---letting the juices flow a little in the battery. Then hit the ignition.
I think you need a battery charger, or, at least a set of jumper cables.
You mentioned you drove it for a while the night before...did you happen to notice the alt guage--whether it was charging or not?? It could be your alternator.
11.3 volts sitting is not that great, in fact, it is pretty poor. It should show over 12 volts. When running, it should show about 14 volts w/ alternator running.
Just a few thoughts. SgtDel
aka "Andy"
www.delbridge.net
1979 Big 10 383 stroker
1991 Blu 'Burb 3/4 ton 4x4