A new battery does not mean a charged (or even good) battery.
But do you have alternator output? On a car that is off, put your DMM on the battery terminals. Look for ~12.6 volts. Once started up, look for 13.5+ volts. If you are below 12.6 volts while the car is running, you are running off the battery.
also, make sure no loose wiring connections or wires are present. I had a wire that was not seated all the way in the harness for the alt., and the battery would die within seconds. It didn't look loose, but it was....
Just to expand on what he's talking about ...
A diode is a one-way valve for electricity.
The diode only allows current to flow in one direction.
A/C = alternating current
D/C = direct current
An alternator generates alternating current (a/c).
The diodes in the alternator "turn" the a/c into d/c to recharge the battery, because a battery is a D/C circuit power source.
Like srothfuss said, if a single diode or group of diodes (rectifier) is shot it can discharge your battery quick enough. A fully charged battery usually takes longer than 5 minutes though.