Yes, there's an arrester where the line comes into the house. After a hard reset, the phone LED remained on. When you pick-up the phone, get a dial tone, and then connect the Omni IIe phone line, it abruptly drops the dial tone.
So, I called Leviton to have them troubleshoot with me. Hard resetting (remove the 24v power brick and the battery, let sit for a half-hour) did not fix the problem. The phone LED remained on, and (again) connecting to the telco dropped the line. Measuring the impedance on the red/green revealed the problem: almost a dead short.
Leviton repairs these boards, and you can buy new ones (a bit amazing that 10+year technology is still manufactured as "new") on Amazon for $699 (cheaper than anywhere I was able to find) and delivered in a day.
Take care to map the connections EXACTLY. Also, note that a replacement board may have the jumpers set differently. My advice: take pictures first, then label EVERY connection. Several are bunched together, and for those put a small nylon tie on them.
Before you start the process, download ALL your settings. Once you've done that, and installed the new board, connect the software (serial, default code is 1111 or network by using one of the keypads to enter the IP, Port, and encryption keys). Reload the system, and you're back in business.
Hope this helps others.