Each of the four probe rings is connected to -1.25V by a 10k resistor so with the scope powered off you should be able to measure the resistance between each pair of probe rings at not more than 20k. If the pairs involving Ch1 give different results to the other pairs (ie Ch1-Ch2 is different from Ch2-Ch3 etc) then there is probably a break in the wiring of the Ch1 probe ring. There is a three way ribbon cable emerging from the Ch1 attenuator, if you unplug this you should get zero ohms from the probe ring to pin 3, the orange wire.
The next check is resistance from the Ch1 probe ring to pin 1 of the analogue multiplexer chip U2601. This should read 10k, if not measure from pin 1 to either side of R2704. If all the resistance checks prove OK then as a last resort measure the voltage on pin1 of U2601 and see if it changes when you plug the 10X probe to channel 1. To compare with a working channel measure pin 5 of U2601 while plugging the probe into Ch2. If you don't find anything wrong by now you probably have a dead U2601 since everything after this is common to all four probe channels.
Roger