The HP 54510A is supposed to be an older 250 MHz digital scope, not a spectrum analyzer. It will probably have an FFT function, but this would be severely limited in dynamic range for spectrum analysis.
With a bad ADC chances are it would be really difficult (maybe impossible because on unobtanium parts) to repair.
There is still a chance that it is something simple (e.g. clock or supply), but it is a gamble - so almost nothing looks like the correct price.