If you could find out the brand and model of the drive you could download hardware diagnostics from the manufacturer's site and run them on the drive and see if it's indeed bad.
On a new hard drive, you'll have to partition and format it before you install the OS, but I think Windows Me setup goes through that. I never used Windows Me, but I believe the CD-ROM was bootable. Just make sure the boot order in BIOS is set to CD-ROM first. To get into BIOS you may have to press a key like Del, F2, or F10 during the POST screen.
If for some reason the CD-ROM isn't bootable (or your system is so old it doesn't allow booting from a CD), go to
http://www.bootdisk.com/ and get the floppy image. Then create your floppy and boot from it, and it should let you partition and format, then pass control to the CD-ROM drive for setup.