Where to start?
Your main circuit breaker did not trip because the PC did not draw enough current to cause it to trip. PC power supplies are around 70% efficient. The typical 250 watt PC power supply should never draw more than 3 amps (at 120 VAC). Most have an internal fuse that would blow long before a circuit breaker would trip.
If there are no signs of burnt components on the modem or motherboard, it may be just the power supply that is dead.
The failure of the power supply may be coincidental to installing the modem.
There are a number of ways that installing a modem could damage a PC.
1. Wrong style connector. If you were to force a PCI card into an ISA slot, or the other way around. The PC might still power up. It would take just a little bump to short out circuits on the connector.
2. Poorly mounted motherboard. If the motherboard is not properly supported, or is on short stand-offs, installing a plug-in card could cause the bottom side of the motherboard to make electrical contact with the case. This could cause a catastrophic short.
3. Undersized or weak power supply. If the power supply was near it's maximum output, adding a plug-in card could be enough to cause an over-current situation. This would be worse at a "cold" start than a warm start.
4. Modem failure. The most "common" failure for a modem is from a voltage surge on the phone line.
If there was a lightning or wind storm between the 2 times turning the computer on, a voltage surge on the phone line could have damaged the modem. Then, when the PC was turned on, the modem attempted to draw more current than the power supply could provide.
Still, my guess is that the power supply just happened to fail the day after the modem was installed.
It is fairly easy to swap in a different power supply to see if it is the problem.
Chas