Windows 98 using USB CD-ROM

That old of a computer more than likely will not boot from USB. You will need to install a cd-rom to install, as far as I know. Been so long since I used 98.

1 IDE port can handle 2 ATA devices, ie;1 hdd + 1 CD-Rom or 2 hdd's. It's probably not worth messing around with, unless you can get hold of a cheap or free cd-rom.
Most new drives are DVD's which I doubt it will recognise.

I don't know... 1 IDE port and no floppy usually suggests a new computer, not an old one. Old computers always came with at least one floppy drive, but sometimes not an optical. It's really weird for a new computer to not have an optical drive though... are you sure there's no CD / DVD drive?

Add a Cd or Dvd drive on P-Ata if you can. Dvd drives run as Cd through compatible standards.

As W98 has native (but bad) Usb support, you may try to install W98 quite normally from its Cd in a Usb Cd drive, provided the Bios can boot on Usb.

Other possibilities involve complicated operations.