How to set routing on XP machines with WiFi and LAN

I have setup my new PC with a WiFi connection to the cable modem and 100M LAN for internal transfers of large files. The problem was that after a reboot, despite WiFi being connected and up, all Internet connectivity would fail.

It looked like a routing issue, and it indeed was. Apparently, due to how Windows determines the metrics of the interfaces available on the system, the LAN would always win and LAN router would be chosen as a default gateway, instead of a WiFi one.
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