It sounds like you did everything right. The "a43 File Management Utility" is the equivalent of windows explorer and would normally be able to see your files. I am surprised that since you said good ol' DOS could see them that the "a43 File Management Utility" could not. Did you DOS by itself, or some DOS based program, such as Norton Disk Editor or ...?
I'm guessing that it is a FAT partition rather than NTFS. (DOS by itself can see only FAT.) Obviously there are some serious problems with the partition. Anything is possible but since DOS can see quite a bit of the drive, it is very likely that the damage is limited to the system area of the drive. The MBR must be intact, or you couldn't see the partitions. It is most likely that the damage is in the Boot record of drive C: and possibly some FAT(File Allocation Table) damage. Since FAT partitions have 2 copies of the FAT, it is possible that DOS is using the second FAT table, while the Windows "a43 File Management Utility" is unable to.
But that doesn't help you recover the files. It is very likely that DOS's scandisk or Norton Disk Doctor(the command version) could identify the problem and fix the errors on the drive. Then Bart's PE should work for you. That "probably" will work,... I say probably BUT...
While Scandisk and NDD are awesome utilities and can usually (maybe 99% of the time) correctly identify and repair a drive, I have used both and on one drive NDD totally messed it up it up and made further data recovery virtually impossible. Anytime you write to a drive with data on it, you are taking some risks, and in the case of Scandisk, you are trying to repair the drive itself. Since the utility that comes with Bart's isn't working, you have 2 choices that I can see. The quickest is to use scandisk and let scandisk repair the drive, then boot with Bart's and hopefully the files are visible. There is a good chance that will work.
The safest method is to connect the HD to another computer if possible(possibly not on the laptop), Or...
Get data recovery program that is capable of reading the drive and analyzing the file system without making any changes to the drive itself. You would then make a new boot disk(Bart's PE) with the recovery program (possibly GetDataBack) on the disk. (Or the program could possibly be copied to an external drive and run from there.) This method will most likely cost a few bucks and will take considerably more time, but is the safest. It depends on how valuable the data is to you and your father.
It's up to you, but ... I think you might want to try scandisk(or NDD). They usually do the right thing.
Expect a message or 2 such as:
"Your boot record is corrupted. Do you want to repair it?"
"One of the copies of the FAT is damaged. Do you want to repair it?"
Say yes and hope for the best.