The peripherals will be fine but the motherboard is the problem.
ATX power supplies use a different motherboard connector and have a different voltage specification. They also don't allow for a "hard power switch" at the front of the case like on AT power supplies. Instead, their power switch connector is wired through the ATX power connector that plugs into the motherboard, and essentially, the motherboard turns on the power supply! (Once it detects a push from the case button.)
The ATX specification also calls for a different case layout to allow for motherboards with I/O connectors attached directly to the PCB. So you'll have to change the case, but the hard drive, CDROM, floppy, etc, will be OK.
Modus