@nomadradio - Message #9
I forgot to mention 8V regulator and protection diode were checked.
But then too, you're testing for Continuity - so the VOM will act differently than a higher scale resistor reading check.
Some meters even reverse the polarity of their leads during this test - for even the 9 volt battery can blow parts on the board - LED's as well as different Zeners and small SMD resistors can blow from the current the typical DVM of just a few years ago can send thru the leads. Analog meter types can do that kind of damage too.
The main problem you're seeing
@Low_Boy - is the very thing you posted about - the caps.
Some are pretty huge, as you find out - so they tend to take in all the current - but you have at least 25 larger value Electrolytic's in there awaiting the other 24 to recoup a charge which isn't going to happen for a long long time while you're busy trying to figure out why the VOM is acting this way - they are simply, greedily, current monster - munchers accepting what the DVM put out and are asking for more.
Part of this problem? The 7808 - when it's waiting for power, there is a special low-cutout circuit that allows the device to be passive when there is not enough power to regulate. So when the voltage falls below 8~9 volts - the threshold to operate isn't there - so the device acts like a short - but it's not - it's the cutout working to protect the parts on it's output side.
Inside the 7808 is a reverse biased Zener - it's there to protect the input from reverse polarity and overvoltage - you can see it in action if your leads on the continuity checker "reverse their polarity" for testing. You're seeing the internal zener as well as the cap charging - at the same time and the meter shows you a short because of this.
There's lots of stuff going on - but I'm glad you take the time for that procedure - for many don't and suffer catastrophic failures from the "patient" surviving the surgery - but dying on the table during the power-up procedure...