Odds are you are seeing that the connections on the back are parallel connections. The wiring inside the cab is not necessarily so. It's not unusual to use both serial and parallel connections with multiple speakers depending upon what ohms the speakers are.
For instance for a 4 ohm 410 cab you might have 4 ohm speakers to start with. Then you could have each pair of speakers wired in series so that each pair has an ohm load of 8 ohms and then wire the two pairs in parallel, which will take those two 8 ohm pairs down to a 4 ohm total cab impedance.
If you are using 8 ohm speakers in a 410 you could wire those pairs in series to make 16 ohm pairs and then wire the pairs in parallel to end up with an 8 ohm impedance cab. You could also do it the other was around wiring the pairs or 8 ohm speakers in parallel making them 4 ohm pairs and then wire the 4 ohm pairs in series resulting in that same 8 ohm impedance cab.
Then, when you add a second group of 4 speakers to make it an 810, you open up a whole other level of options because you can wire two groups of 410's at 8 ohms for each group together in parallel to equal a 4 ohm 810. Since that SWR 810 uses 8 ohm speakers, odds are that was how it was done.
If you are not familiar with how these cabs are wired, you need to either get a wiring diagram from SWR or get someone who really knows how to wire cabs to check it out for you.
You also may want to check the L-pad, which is where all the wires hook up on the inside of the backplate. If it died it could cause that problem too.