My laptop won't accept my external hard drive...Windows '98.... it keeps asking me to reformat it! How can I get my old laptop to accept my external hard drive without having to reformat it?

Windows 98SE usually works OK with USB devices, the non SE version is more troublesome. Unlike later versions 98/98SE do need drivers installed. There are some generic versions available or check with the drive manufacturer web site.

Win 98 can't access NTFS drives without NTFS drivers being installed. You need to pay for these if you want read/write access, but you can recover files (read-only) with free apps from DOS (if the drive is recognized). You may need to connect the external temporarily as an internal in order to recover the files you want. You can then remove the partitions, create new ones, format FAT32, and access it as an external from 98.

NTFS for Win98
http://www.sysinternals.com/Utilities/NtfsDos.html

I do have Windows 98SE on the laptop but the hard drive is formatted in FAT 32 (my external hard drive is NTFS). All the drivers for my external drive have all been installed in my laptop. Are there other drivers that you're talking about that I might need?