The power supply is the least likely culprit. While power supplies do flake out occasionally, their behavior in those circumstances tends to be much more erratic. Either that or they just die suddenly. You can count the power supply out. The next thing you want to do is eliminate the modem as the culprit.
Modems are easier to mess around with than motherboards.
Additionally, the Zoom PCI is a Winmodem, and winmodems are notoriously flaky . First, grab the latest drivers and install them. I know this might sound obvious, but people with OEM machines like those from HP are finding that this is a big help for just this kind of problem. If the problem persists, try moving the modem to a different slot on your board. The best way to eliminate the modem as the problem is to grab yourself a hardware modem and try that.