At this point I am assuming you are powering up the HM with the USB cable to the rPi? Do you have the display connected with the header going from board to board or do you have a ribbon soldered in? If you have a ribbon on the display make sure you didn't break a wire loose while fiddling with the voltage regulator.
You can always check if the rPi is working by unplugging it from the HM board and booting it up off USB power with a monitor connected to HDMI header....
I'm about the same age and have been messing with electronics about as long as you, when soldering up the HM I was surprised how hard it was for me to see if the solder work was good (had to use a magnifying glass too). At first I thought it was my eyes, but my vision has been and still is pretty good. Eventually I came to the conclusion that the purple board makes it hard to see where the traces stop and the solder starts. Some of the solder joints and traces are pretty close together on the HM board as well. I had set out on the job with my butane portasol iron but later realized a regular soldering iron would have been more suited for this job.
Using the digital camera to shoot a high res closeup is indeed a great way to check up on your solder work, you can zoom in on the picture and see the solder joints and traces really well compared to the naked eye or even using a magnifying glass....
Now that you know the +5V regulator is blown, do we have any idea what caused that to happen???
If you are ordering another +5V regulator might as well throw in another shift register too, they're cheap enough... I would buy a spare oscillator as well since I was able to break mine loose after too much fiddling with the board. (in and out of the case too much, I guess it got pushed back and forth one too many times). The parts are so cheap, might as well avoid the frustration of needing one little part and buy some spare parts while you are at, at least that's the way I think....