Yeah, as shakalnokturn mentioned, if the fault is common to all channels, I'd be looking at the internal signal generator for problems, after doing the leaky capacitor dance.
Also, I'm not 100% sure, but if the 500 series is similar to the 600 series in that all channels end in a single acquisition chip (rather than one per channel as in the 700 series) that's another potential point of failure that could affect all channels.
Easiest next step after doing the capacitor thing is to grab the schematics and poke at the internal signal generator. You might even have a corroded trace or two, it's not uncommon with these leaky capacitors.