Your Wish:

"Auto re-boot modems that don't answer in 6 rings"

ARR Automatic Ring ReBooter

Reboots AC Power on Dial Lines That Don't Answer in Six Rings.

IPC International Power Controller

AC Power reboot over ordinary phone lines or automatically via an RS-232 port for unattended remote equipment. Uses internationally standard IEC connectors.

K-RRC Key-Based Remote Reboot Controller

Control AC Power or press the reset button on remote equipment out-of-band, over ordinary telephone lines. Other calls pass through transparently.