For home made packs, you need to worry about the 3rd terminal. That's used to detect battery overheating using a termistor. If that isn't wired up properly, the Pleo may be shutting down after booting, thinking that the battery has overheated.
Other advice:
> I have taken my volt meter to the battery pack I made and show that it is charged showing 7.8 vdc.
That is normal. Reading a fully charged pack with a voltmeter with no load will easily be 7.6 volts or higher.
If you can't test it inside of Pleo, try placing a small load across the battery terminals (eg: a small low voltage light bulb). The voltage should drop a little from 7.8 volts, but should be well above 7.2 volts.
> I put the batt. pack in and pleo only works for about 10 - 20 seconds.
Does it move and make sounds at the start? (when you turn it on, it should take around 10 seconds to boot up the V1 software)
What happens after 10 or 20 seconds?
Does it shut down, make a noise or just stop?
If it crashes during movement, it may be draining the battery when turning on the motors. Or it could be the movement is causing loss of battery connection. If possible check the running voltage in your home made pack (or if possible the current drain)
> I thought I would give upgrading the software a shot.
Upgrading requires that the CPU runs for a while, but the motors don't move, and IIRC it doesn't check the battery temperature.
If none of those suggestions help, try one of the SD card entertainment personalities (like Babe
http://www.aibohack.com/pleo/babe.htm, or one of the others on PleoWorld)
They will use the hardware in different ways.
Good luck.