Hopefully this one will prove to be a better experience than the other unit. Anyway, you should get a SSR solid state rectifier for using with the variac so you do some voltage checking and also helps with capacitor reforming, although this unit will probably require all the electrolytic caps to be replaced.
First thing i do with a unknown unit is to check the power cord and then the fuse. Since the power cord was cut you need to replace it. ( some sellers cut the cord to "absolve" them from litigation because a person plugged in the unit without having it repaired) . Sometimes the seller cuts it to indicate a serious problem but they would usually say what that is. I use a cord with alligator clips at one end so i easily clamp it onto AC cord inputs.
Second thing is to do a visual check of the transformers and components looking for obvious faults, burnt out resistors, goop leaking out of transformers, blown out capacitors, white stuff leaking out from electrolytic caps, obvious signs of a short like a burn mark on the chassis, loose or broken wires .
Next pull all the tubes and have them tested. With no tubes in the amp and using your ssr instead of the tube rectifier and the variac and your meter. Put the variac on 10v or 10% and turn on the amp. Since there are no tubes and little load the B+ voltage will be quite high at pin 8 of the rectifier tube socket, about 40 to 50vdc. If you have very low or say half the voltage you need to check for problems. If you don't have any issues you can add on 5 more volts to the variac after about 5 to 10 minutes of letting the lytics reform. I would do this until you reach 60vac.
During the slow incremental AC increases use your meter to check the B+ as it goes through out your circuits. As the dcv goes thru each resistor/cap voltage tap you need to check that it is. If at this point everything seems to be ok, no bad burning smells, no resistors starting to smoke, no electrolytic caps getting warm ( if the can cap is getting warm at this point then it is almost ready to fail), You can go on to the next step. After turning off the amp!
My next step is to install all the tested tubes in their proper sockets including the rectifier tube, and properly hooking up some cheap, but good sounding speakers you don't mind ruining. When all is hooked up properly turn on the amp or variac and monitor the b+. It will probably take several minute to come up as the rectifier slowly starts to conduct. The b+ will now be lower since you have tubes to load down the transformer. If you don't have any B+ or very low volts you need to check why. You should be getting around 150 to about 200 vdc. Hopefully, you have no problems and can proceed with incremental voltage increases.
At about 75 vac i plug in my walkman cd player as a signal source into the AUX. rca sockets. It should make a nice reassuring hum when the plugs go in. Turn on the player and if your stars are in alignment and the voodoo priestess's incantations were effective, and with crossed fingers and crossed toes you will have some music coming out of your speakers.