When you say that Windows sees the partitions, can you read and write to them just fine from Windows? And you can still boot into Win98SE on sda1 OK?
How about trying to mount a couple of your logical partitions and see if that gives the same result:
If that doesn't work, try:
sudo mkdir /mnt/sda5 /mnt/sda6
sudo mount /dev/sda5 /mnt/sda5
sudo mount /dev/sda6 /mnt/sda6
And if that doesn't work, then I would boot into Windows, open a terminal ("cmd") and do:
sudo mount -t vfat -o force /dev/sda5 /mnt/sda5
That should give the drive letters of your data partitions, and for each one, how about running:
Replace "D" with the drive letters of the data partitions, and also run chkdsk on each partition as many times as it takes until it reports no errors. Let me know how that goes.