Hey, mbguitars!
I picked up my DL4 in 2005 and it eventually started restarting/rebooting randomly. Since I couldn't rely on it, I put it away and kind of forgot about it. I pulled it out last week though and tested it. Same thing happened. I use the Line 6 power supply it came with as well. I can't remember if this happens when I'm using batteries though so I might try that out this weekend. That might be an option for on stage use, but not a real solution.
I also checked the solder joints for the power connector. They all looked fine. One might have been a little cold, so I hit them with the soldering iron to touch them up. That didn't fix the problem though.
And I recommend putting in a support ticket as well. I haven't heard back, but I just sent it in yesterday. I'll keep you posted once I find something out!