Restarting Modem/Router Is Crashing Our Snow Leopard Macs

We recently upgraded our broadband service to a "bonded" DSL plan (i.e., two phone lines are used for data transfer). Our old modem + Time Capsule set up was replaced with a Pace 5168N-110 Gateway (combined modem + router). Our internet connection since changing services has faltered and restarted itself a few times. When the internet connection comes back on line, our two 10.6.8 Macs become mostly* unresponsive and have to powered off by brute force (holding the power button for 5 seconds).

Today I simulated an internet restart by power cycling the Pace gateway. The 10.6.8 Macs were

• OK when the gateway was powered off
• OK when wifi and ethernet came back on (one connects via the former, the other via the latter)
• stuck when the internet came back on

The affected machines respond to some mouse and keyboard input, but are largely unresponsive. Menubar clocks are frozen, the cursor becomes a "beachball", system menus are unavailable. If a screensaver was active, no input will wake the monitor. If a login password is required to unlock the screen (i.e., from sleep), the password can be entered, but the login screen persists.

By contrast, our one Yosemite machine was unaffected two power-cycling tests this morning. That said, I know it suffered at least one crash similar to the above which, I believe, corresponded to an internet outage.

Unfortunately, I haven't been able to make sense of anything from the Console log; there are no entries from after the system becomes unresponsive.

Any ideas?