Ok, to all the wrong answerers posted here, sit back and learn something ...
To the Asker - The problem You are having has nothing to do with downloading drivers for the external hard drive. No matter what You download it won't recognize, so stop trying to find something else to add to the system and clog it with useless files, info, and potentially damaging software.
The problem You have is related to the 2 (and only 2) facts I'm about to list here.
1) Windows 98se will not recognize a partition size above 20gigs on ANY hard drive - period. Your 300+gig drive is probably set as a single partition, Win98se won't see it, and even if it can find it, it will cause system errors for all data above 18gigs.
2) Win98se required all partitions to be in the FAT32 format, and most new systems (above WinME/Win2000) use the better performing and more talented NTFS format. FAT32 had a size limitation of also 20gigs. This wll also be compounded by any hardware limitations of Your actual hard drive controller (on the motherboard) in a Win98se system that will probably be around an ATA66/ATA100 IDE controller at best.
The best possible solution to simply get Your current data from the drive in the system now (quick and dirty - no case opening involved), is to use another system that's running a newer OS (that will recognize the drive automagically - XP is fine) and create 3 partitions on it.
The first partition will be 1 primary partition of 128gigs, You won't format this drive (so 98 won't try to see it), it will be done during the setup of XP, as an NTFS drive.
The first extended partition will be the rest of the drive MINUS 17gigs of the drive's space, listed as 17million megs, not the actual numerical 17gigs. This will be extra storage space, and is necessary because XP (any flavor) won't recognize anything over 136gigs of space on a hard drive partiton. I set it to 128 for performance and safety of data reasons You'll learn down the road.
The final partition (the leftover 17gigs) will be formatted as a FAT32 drive (FAT16 if You're EALLY cautious), and when You plug the drive into a Win98 system, it will recognize the partition, although it might not autoplay it for You.
Use this partiton to do a complete backup of the C: drive in the Win98se system, and then You can simply palce this drive into Your system with the Windows XP CD. The setup routine will ask You which partition You want to install it to, pick the first (primary) 128gig partition and You're off and running.
After You have all Your new XP releases of software you want to use, instead of trying to run all Your Win98 stuff through a dual-boot setup, they've updated that process as well. The new method involves a piece of software called "Microsoft VirtualPC 2007". It's a free download from Microsoft.com and basically uses a swapfile to seem like another hard drive partition, and simulates specific audio/video hardware to run other operating systems / Windows versions.
When that's finished, You still have all the old files from the Win98SE system on the same hard drive You're running XP from. Assuming You took the hard drive out of the portable case and installed it directly into the system. Otherwise it's just all on the exernal drive's FAT32 partition to copy to the XP drive and You can simply format the first 2 partitions for use.
Good Luck!.