Random thoughts time.(is there any other type)
While you're playing it might be worth keeping both probes and both channels on X1, to eliminate one variable.
Is it the same shape with AC/DC ch1 coupling.
View the 1khz on both channels at the same time, just in case ch1 is loading the signal somehow.
Enable the digital filter on ch1 and try some settings to see if they change the waveform, set a LP of a few Mhz, if the filter settings have been corrupted somehow rewriting new values might fix it, including the on/off.
Try capturing some fast rising edges, just from a 1.5V battery would do, ch1 only seems to rise about 200mV before it has a problem.
200hz to 5khz 1V square waves from a sound card might help to give a clue what it's doing.
Well I did say they were random!