Energy, voltage regulators and capacitors... HELP!

vander:
I measured the voltage of my batteries and found that four of them had between 1.10v and 1.20v. One had .80v and one had -.02 volts!! I didn't know it was even possible to drain a battery to the point of negative voltage!!

That's because the strongest batteries can reverse-charge the weakest one eventually.

vander:
Did some reading and found that it's a common problem when the batteries aren't all the same brand or even the same charged voltage. If one drains faster than the others, it gets negative voltage if connected in series.

That's a big problem since i expect to keep my design turned on for at least one month.

Just make sure the batteries are all from the same blister pack.

vander:
Now I'm considering changing to a 6v 4.5 amps lead battery. I have to see if the motor turns with less volts . The only problem is to find the right voltage regulator.
I don't know if I keep the lm7805, the 78L05 or another regulator... What do you think?

Neither, you need a low-dropout regulator. I have used TL750L and MCP1702 for this sort of project.