F000:C7E0 25 C8 FF 05 43 50 32 30-34 34 08 4A 44 2D 45 32 ...CP2044.JD-E2
F000:C7F0 38 35 30 50 05 43 50 32-30 36 34 07 4D 4B 31 31 850P.CP2064.MK11
F000:C800 32 32 46 43 05 43 50 32-30 38 34 08 4A 44 2D 45 22FC.CP2084.JD-E
F000:C810 32 30 38 35 4D 07 4D 4B-32 30 32 34 46 43 05 43 2085M.MK2024FC.C
F000:C820 50 32 31 32 34 07 4D 4B-32 31 32 34 46 43 BA F7 P2124.MK2124FC..
The list of drives in a 3.20 BIOS. (CP=CONNER, JD=JVC, MK=TOSHIBA)
There is one problem though; in 1992 a 200 Mb. harddisk (the maximum that the T4400C was produced with) was state-of-the-art so the logical maximum of 528 Mb. that the disk routines in a PC BIOS could access was not a problem.
It is nowadays. New schemes to work with larger harddisks were invented (LBA mode and Enhanced IDE) but no T4400 BIOS include these so even a BIOS 3.50 will only be able to work with 528 Mb. even if the actual disk has more capacity. To get around this you either will need an adapted BIOS, which some vendors sell together with a large drive, or you will need a software solution like EZ-Drive from MicroHouse or Ontrack's Disk Manager.
Another option for your storage needs would be an external ZIP drive, connected to your parallel port. Also, there are a number of suppliers offering hard disks that connect to the parallel port. Don't count on these being fast performers though; the parallel port is too slow for that.
If you can get a DeskStation IV you can install a large harddisk in it. In that case get an ISA EIDE harddisk controller card that has its own BIOS extension and install both in the DeskStation.