[G6Tanuki]

Not sure about your specific beastie but usually these have a character-generator chip that holds a matrix of 1s and 0s to represent each displayable character on a suitably-sized matrix 9x6 dots or similar] - if you're getting a locked picture with recognisable characters [even if gobbledegook] displayed on the screen then it at least shows this character-generator is OK [I've known them go bad].

Easy way to test that the CPU clock is running without imposing any possible disruptive load on the clock circuitry is to listen for it with a shortwave receiver! The clock freq will be marked on the xtal can - set your SW radio to SSB or CW then attach a short length of wire to the antenna terminal and dangle it near the clock xtal. Tune around a few KHz of the marked frequency and you should easily detect the carrier as a raspy buzz [it's near-enough a square wave so don't expect a 'T9' note!]