Okay - some weird behaviour there alright
A few more things to check.
1. How are you powering it - what is the Voltage / amp rating of the source of power to your gear?
2. Can you check the power supply with a Voltmeter - even the $9.95 ones from Jaycar or Dick Smith are fine for this task - do they match rated voltages and ampages - check its not a faulty power cable into the mount causing a voltage drop
3. Are the pins from the SS2K to the mount all fine - none corroded or bent on the hand controller - no lint in the cable messing up a signal?
4. Have you asked if anyone around you has a spare SS2K you can borrow for a night to confirm its the hand controller - not the mount - acting strange?
5. You are dead certain the new battery is of the correct rating, orientated correctly and well soldered to the unit? Did you test it to confirm it was okay before you soldered it into position? Did you use minimum heat and/or heat sinks (i.e. alligator clips) when you unsoldered the old battery and re-soldered the new?
6. Everything fitted together well - and all spacers and insulators were re-inserted when you fitted the SS2K back together after changing battery - i.e. nothing was obviously touching or shorting between the two boards?
I think it might be time to definitely describe this situation to Chris Erickson who moderates the Yahoo Groups SS2K board and ask his views
https://groups.yahoo.com/neo/groups/SkySensor2000/info
and/or
https://groups.yahoo.com/neo/groups/ss2k/info
Will think some more of what else to try next!