Sounds like the floppy disks have lost their data. Can happen over time specially with lightning, cell phone towers, etc. Any electro mag radiation slowly degrades the data/format, etc.
Most home written floppies were designed for a bout a 10 year life span for data integrity (early CDR had about 20 years but by late 1990's was closer to 40 years)
Professional written floppies (like from Manufacture, Microsoft, etc) can last decades if properly stored.....

I think it's unusual than none of the disks work. Some time ago I backupped a lot of C64-disks and they pretty much all worked. Some had errors but in general pretty much all of them were readable. However old 5.25" disks are surely more reliable than Noname 3.5". What disks exactly do you use?

Were they stored properly? Maybe there is mold or any other spots on the surface? (Take a magnifying glass and manually rotate the disk to inspect the whole surface).
Maybe your old drive or this one is misaligned?

And if you use Win9x for that you should be aware about this:
"Windows 9x by default rewrites the OEM identifier in the boot sector of every floppy disk that it accesses, even if the access is something as simple as listing directory contents."
(seems dead at the moment, so here is it on archive.org)

Good points ! Possible the heads are slightly out of alignment so cannot read the disks written by a different floppy drive. I would try a another floppy drive to see if the issue is the same.

GunKneeNeon wrote on 2023-05-13, 00:12:

I have a lot of old floppy disks that I want to read data from. However, none of them can be read successfully by my floppy drive. In Win98, it says that my floppy has not formatted and suggests me to format now. In MSDOS (entering by press F8 when booting then choose Command Prompt Only entry), it says General failure reading Drive A. I was thinking that my drive is dead and googling around to try to fix the hardware. But it's not! If I reformat the floppy, the drive functions very well. I can then do normal file manipulations smoothly. Now the problem is how I can read my old data using the drive. I find this explanation from other forum: ""General Failure" is a catchall error for floppy errors. It could mean that the boot sector doesn't conform to later DOS standards (you sometimes get this when you try to read a DOS 1 or 2 floppy on a later version of DOS)." This is not my case, I never used these disks under old versions of DOS or any other older systems, but it may be a clue that the boot sector of the disks have compatibility issues with my win98.

Any help is appreciated! Thanks in advance!

I recently had the exact same problem even after swapping drives. It was the cable!

Interestingly none of my retro PCs could salvage the disks that had been attempted to read with the dodgy cable. But my windows 11 machine with USB floppy was able to format them and they would then work again..

Horun wrote on 2023-05-13, 13:16:

Good points ! Possible the heads are slightly out of alignment so cannot read the disks written by a different floppy drive. I would try a another floppy drive to see if the issue is the same.

I've encountered that before, the 'unique' floppy drive which can read/write disks it has formatted, but no others!

Horun wrote on 2023-05-13, 01:06:

Professional written floppies (like from Manufacture, Microsoft, etc) can last decades if properly stored.....

Maybe you're right, I tried the drive with an official anti-virus software disk. This time it recognizes the disk, but when I type dir, it lists the files then throws an error and I can't do anything more than that. It seems the professional written one is literally more readable than the others.

Horun wrote on 2023-05-13, 13:16:

Good points ! Possible the heads are slightly out of alignment so cannot read the disks written by a different floppy drive. I would try a another floppy drive to see if the issue is the same.

I've ordered a USB floppy drive online to use with my modern PC. I'll be able to check if the disks are failed or the drive head are misaligned.

when you access the floppy disks, be sure to enable the write protect tab. it's possible that you're old system has a boot sector virus active and corrupts every unwrite protected floppies that are accessed

I always wondered who this General Failure is and why is he reading drive A:

On a more serious note, my experience of 3.5 disks back in the day was not very positive. They would sometimes develop read errors between writing them, carrying them somewhere and trying to read them again. Sometimes formatting fixed them, other times some sectors went bad. Bad sectors was annoying, because I used ARJ to create multi disk archives, for which disks with bad sectors were too small.

I still have a box full of stiffies, but have not touched them in years. Networking for the win.

Problem solved!!!
The head is indeed misaligned. I calibrated it using ImageDisk by following the steps in this video and it worked!

The long story:
I've ordered an USB floppy drive online. The new drive read out about half of my diskettes, but it could only list the files. There was only one diskette that could be copy entirely successfully without any problem. Then I tried the diskette formatted by the old drive with the new drive, there was a file copied to the diskette by the old drive. The drive read out the data without problem, that seemed to be a proof that the head of the old drive was good. I then reformatted the diskette using the USB drive and made it a Win95 boot disk. I was wondering if the boot disk can be read by the old drive, yes and no. The old drive saw the contents as if it had not been formatted by the USB drive, the file copied by the old drive was still there. I tried to copy it to HDD and it succeeded. Now the two drives saw the same diskette as totally different ones, they could not see the files copied by the other one and manipulated the contents created by itself smoothly. Then as I said before, I calibrated the head according to the youtube video mentioned earlier. The diskette used for this task was the only one that could be read successfully by the USB drive. The result is amazing, it can read out the data from over half amount of my diskettes, its performance is even better than the new drive!

The drive was bought back in 2000/2001 and the head was misaligned since then. It was the first PC I owned in my life. It gave me an impression that diskettes are easy to fail. I had been downloading mp3s from internet cafe using diskettes that time. Every time I got read errors with several diskettes just written by the drive of the PC in internet cafe short time ago. Now the mystery is solved, it is the drive not the diskettes!

Thank you all, my friends!

Now I'm gonna try to restore the fail diskettes and see if I can recover as much of the data in them.