um... I'm seeing either an error in method doing the measurements, a damaged meter, or a very bad battery.
A standard car battery, you should be able to clamp a meter to the posts then short it with a piece of rebar and NOT go past maybee 7.5v, but would have arcing, sparking and melting going on.
so to see 4.5v dc at the battery hot cable either means bad battery, or bad cables / terminal ends, bad meter, or wrong measuring technique.
Also.. curious.. bat static voltage should be only 12.6.. it will be a little higher right after charging, but should drain off the high charge in minutes to 12.6.. a battery setting at 13.8 is kinda odd.