I hate to dig up a zombie thread, but I wanted to share my findings.
I shelved this project awhile ago and only just recently decided to throw it together and be done with it. I'm using jsgf's latest firmware. I too discovered that my Ice Tube was not running right at all with the backup battery installed. My Ice Tube functioned perfectly without the backup battery. I had the battery installed in the correct orientation, and verified it still held a very good charge (barely used, I removed it before shelving).
At first, with the backup battery installed the display appeared at the lowest brightness. I could go through all the menus and change settings, but there was no buzzer noises and the time never updated. Then, later on, it rarely showed anything on the display.
I poked at it with my oscope with the power removed and the battery still in place, and found the the clock crystal was inactive. The voltage divider was working correctly (~0.75V), and the battery supply was good (~2.85V).
I reapplied power and saw the crystal was still inactive. I shorted the reset on the ISP to ground, and everything came back to life. Display displayed, buzzer buzzed, and time advanced. I pulled the power plug, let it sit for a second, reapplied power, and nothing. Hit the reset, and bam, all good.
Here's the weird part. I left the battery in, kept the power plug in, and turned off the power strip the wall-wart was plugged into. Turned it back on, and everything returned to normal. If I violently toggled the power strip I was able to induce the error sometimes. Every time I unplugged the Ice Tube from the wall-wart I induced the error.
Either we got a bum part someplace (I remember double-checking the parts list before I started so I'm fairly sure everything was correctly shipped), or our 168's are particularly sensitive to supply voltage changes. Any thoughts?