OK, I found a workaround that enabled me to salvage most of the photos, if not all. Here's how:
1. In PartitionMagic, I made a bit of room on my hard drive and tried to copy the second partition on the SDHC card to the empty space to see if I could see the photo files on the hard drive. I received an error message that there were "too many errors."
2. Just to be on the safe side so I wouldn't accidentally wipe out all the photos, in Computer Management, I did a backup. I noiced that there were a number of multi-MB files with the extension ".CHK."
3. In Computer Management, I did an error check.
4. On the SDHC card, I ended up with a file called "FOUND:000" with 292 objects, all with the extension ".CHK." These were listed in Windows as Recovered File Fragments.
5. I copied a couple of the files to my hard drive and changed the extension to ".jpg." Then I opened one in Windows Picture and Fax Viewer, and there was the entire photo! So now I have 292 files, most of which are of large size, some of which are quite small but may be relics of photos I deleted, just to keep the number sequence in the camera going. I will have to go through the files, looking at the photos on my camera, to figure out the real numbers and give them the proper extensions according to whether they are JPG, RAW, or video. But at least I seem to have most of the ones that are on the card, and maybe all.
6. Just to see, I cloned the second SDHC partition to my hard drive (it worked this time), but when I looked at it, there were still no original photo files there, only the CHK files.
7. I restored the backup file to a folder on my hard drive, but there again, there were no photo files, only the CHK files.
Well! Obviously I will not be using the PNY card in my camera again; I will use the 8GB Ridata cards, which I know work. But at least I managed to retrieve most of my files!