It would obviously be great if you could find a repair manual or schematic. National was a brand name used by Panasonic, so the Panasonic VP-5260A is the same thing as your scope.
This site may have a schematic if you register:
http://www.radiomuseum.org/r/panasonic_oscilloscope_vp_5260a.htmlThe fact that in ALT mode you do get a CH1 trace and no Ch2 trace suggests a few things :-
The scope's horizontal and vertical drive circuits probably work fine
Both of the channel stages seem to be faulty.
It is likely the CH2 output is permanently stick high or low - off the screen anyway
Ch1 output is the correct value, but for some reason, no signal gets from the input to the output.
I would open it up and see how accessible the input channel board is. Be careful working inside the scope. Capacitors in the power supply may have some nasty residual charge, and the scope tube anode (the high voltage cable that probably connects to the side of the tube somewhere) is probably storing a charge of thousands of volts. Just don't try and unplug that cable.
You will have almost identical circuits for Ch1 and Ch2 and if your lucky, they will have used identical board layouts for both. It will make it very easy comparing one channel to the other.
First look for any obvious physical damage - burnt components, exploded or swelling electrolytic capacitors, burnt switch contacts. If someone has put 1000V into an input, there may be widespread damage and you may have to ask yourself if it is worth repairing.
If it all looks OK, you could grab a multimeter, put it on the diode test range, and start testing all the transistors. Compare the readings in Ch1 to CH2. Ch2 could have a shorted transistor, and if so, that will be easy to find. You can check other components using the other resistance ranges on the multimeter. Remember, any difference between the two channels is a big pointer to the problem.
If you cannot see anything and you do not have a circuit, you could try and start working out the circuit of one of the channels if you are keen. The thing is if you can post even a partial circuit, with some DC voltages, we may be able to help. Photos are always welcome here - we can't get enough of them, so when you open the scope up, you may as well take some photos and post them. Pictures that show readable part numbers in IC's, transistors, etc and any text on the board's sikscreen are especially useful.
There could be a power supply problem, but if there were, I would expect to see both channels behaving the same. Just check the power supply components too, but as I said, just watch out for voltages on the high voltage electrolytics. They usually drop down to zero with the scope off, but don't assume that.
Richard