It could be a problem in the software. What do you use? Some peices of software have one method to see what is on a tape and another to restore the information. First things i would do would be to check both the drive and the software. Try making a backup then restoring from it, if that works then the likelihood is the tape. If it does not it could be problem with read heads or the software. Eliminate software next. Try using another peice of backup software there are a few available for trial download. Again try and backup then restore....if it works with other software then we've found the culprit. If not get a diagnoctics program, should be one available from HP and test the drive.
If you cannot get the information off the tape via this then the only other option would be to contact a data recovery agency and have then take the data off the tape at a costly price.
Good Luck