What's the story? Did you get it going? It's not surprising that you had no power and then did have power, that's common with a bad connection. 11.48 volts doesn't sound much lower than 12, but it makes a huge difference when trying to start a vehicle.
It sounds to me like you may have a bad connection at a battery terminal. And you definitely have a dead battery.
Here are some basic troubleshooting steps:
1. Get a charger on the battery, or get it charged at a parts store, or get jumper cables on it.
2a.Turn the key to on. Do the dash lights turn on? If yes, turn the key further and try to start it. What sound does it make? A click? Does the engine turn? No click? Did the dash lights go out?
2b. If the dash lights are not on, or they go out when you try to start it, or they flicker, it is probably a loose connection at a battery terminal.
2c. If you hear a click but no engine turning, and the dash lights don't go out, either your battery is too drained to turn the engine, or your starter is probably the cause.
2d. If the engine turns quickly (full battery) but vehicle doesn't start, you have a different problem.
2e. If you have a full battery and continue to have power (dash lights), but hear no click or engine turning when you attempt to start it, it is probably your starter solenoid.
3. Have a helper try to wiggle the battery terminals and wires while you are watching the dash lights and have the key in the "on" position. What happens? Do the dash lights flicker? If you don't have a helper, you can watch the hood light or the dome light while you wiggle the battery terminals.
If you can get any flickering, you have found your problem. Loosen and remove your battery terminals from the posts and clean with a wire brush, steel wool, sandpaper, whatever you have to scuff up the metal where it contacts the battery posts. Do the same with the battery posts (just don't touch both terminals with the steel wool). Re-attach the terminals and tighten them well enough to keep the terminal from twisting on the battery post. Try to start it again.
If this doesn't work, let us know the answers to those troubleshooting steps.