While I was fiddling with the camera to get that first spectrograph, it began coughing up an assortment of Memory Stick errors, including the dreaded C:13:01 error. Having had this happen several years ago, I knew it came from the ribbon cable contacts in the Memory Stick socket and the only way to fix it involves taking the camera apart.
At the time, I used the guide at http://hbar.servebeer.com/text/f707/, which is now a dead link; you can use archive.org to retrieve it. There’s an exact copy at http://batteringram.org/misc/f707repair/ and a bit of rummaging suggests the same person is running the new site.
Anyhow, here’s my version of the teardown and fix. This is a bit more aggressive than what you’ll read above, in that I disconnect all the cables to get straightforward access to the guts of the camera, but I think it makes everything easier. In any event, re-plugging the cables in those connectors will probably be a Good Thing.
Remove the battery, Memory Stick, and all the straps and doodads. This fix will reset the camera to its factory defaults; you must eventually reset everything, so review your settings.
If your filing system depends on the camera’s numbering system: heads up! This will reset the image sequence numbers; the next picture will be DSC00001.JPG.
Remove the four Philips-00 screws that hold the rear case in place. Note that they are not identical…
Two on the left.

The rear screw on the right side.

The screw on the right side of the bottom passes through the front part of the case.

Ease the whole rear half of the case, display and all, away from the front half, until you can disconnect the three-wire cable from the power jack. A needle-nose pliers may be helpful, but be gentle!

Now things get nasty.
The flat paddle in the lower right plugs into a socket on the display board in the rear case: pry it out if it hasn’t popped out of its own accord.
Disconnect the ribbon cable on the left side by prying the gray latch away from the cable; the ribbon will pop out with no effort.
Put the rear part of the case somewhere out of the way.

Peel the static shield off the main circuit board. The black strip is a surprisingly strong adhesive tape that’s stuck to the ribbon cables along the top edge of the board. Peel gently!

Pull the three cables out of the sockets along the top of the board. The blue cable seems to be much more fragile than the others, but they all come out by just pulling directly upward: parallel to the board.
Unscrew the two P-00 screws holding the main board in place: upper left and center of the board.

Flip the camera over and ease the main board away from the case to expose the white connector on the bottom. This is stuck firmly in place, so try to not brutalize anything around the connector when it pops out.

That leaves only the ribbon cable on the right of this picture (left of the camera) connecting the optical section to the main board. Push the two ends of the gray latch bar parallel to the cable (it is not the same as the connector on the other side of the board shown above) away from the connector until the bar releases the cable and it pops out.
Put the main board somewhere safe.

Now you can actually see the Memory Stick socket behind all the ribbon cables!

Remove the two P-00 mounting screws, one to the upper right and the other to the lower right in the steel retaining bar.
Remove the socket from the camera. Whew!

Here is the offending cable entry into the Memory Stick socket. Pull the mumble cable out.

The socket pins evidently move just a little bit, every time you put in a Memory Stick, eroding teeny divots in the cable contact pads. I generally use the USB connection, so the socket doesn’t see a lot of motion. Your mileage may vary.

I cleaned off the ribbon cable pads with Caig DeoxIT, although I’m not convinced that really does anything in this situation.
This guy dismantled the socket to clean the internal contacts, which would probably make sense while you’ve got the hood up. I didn’t do that this time, though.
Then you reassemble everything in reverse order, after which the camera Just Works. Probably for another few years.
The puzzling part of this failure: the camera has literally hundreds of ribbon cable contacts, but only the Memory Stick cable goes bad. If any other cable failed, the camera would go Toes Up, right? Next time around I may try soldering thin copper pads on the cable or applying a thin backing layer to improve the resilience, but that sounds pretty risky even to me.
If you haven’t done so already, put a write-protected image of your biz card / contact info on every Memory Stick you use with your cameras to make it easy for an honest person who finds your camera to get in touch with you. The dishonest ones won’t change their behavior one way or the other.
Take a picture of your card now: the camera will set up the folders and name it DSC00001.JPG. If you’ve already got such a file, take a picture anyway, delete it, then copy your existing file to the camera as DSC00001.JPG. In either case, write-protect the file.
Memo to Self: next time, take the socket apart and cast some epoxy around the contacts to prevent further motion.