First, I'm curious as to what happened to the original modem? Did it get blown and perhaps something else on the motherboard was also damaged. You didn't explain what was wrong with the original printer but I assume it wasn't related or you would have mentioned it.
Boot to only a DOS prompt then try printing a directory as mentioned in the other response.
If you do it from a DOS window you'll still ahve the same problem because the drivers are loaded.
The command is dir >lpt1
If this works then perhaps there is an issue with drivers or software. If not there's a problem with the port or power.
As far as power consumption is concerned the supply may have correct +5V readings but when printing there may be enough of a current draw that it makes the system halt. Plus there's -5V, +12V and -12 supplied to the circuits. You would need to test with a volt-meter while printing to see if the current drawn is enough to halt the system. Each USB port draws 500mA of current so you do need a power supply that can take this load. Also printing may generate electrical noise which may affect the over-current protection circuit and temporary stop the function of USB port.
You've pretty much eliminated the issue of software problems or resource conflicts because you've reinstalled the OS and it still does the same if connected to USB or parallel. Try printing from the parallel port with the USB port disabled and then opposite.
I'd say either the power supply or the motherboard has a problem. Power supply is easy to swap. Again the modem being out is what leads me to believe this is an electronic circuit issue. There has to be a point where the problem starts and that seems to be it.
