Switch on - expect a thump, but do all cones return to their 'resting' position'.
Is there excessive noise or mains hum?
Do all controls work? Mechanically and sonically. Expect a bit of noise when adjusting, especially linear graphic pots, but these usually improve with use/a bit of switch cleaner spray. If broken they can be expensive/difficult to replace.
Are all sockets OK?
If it has a fan, does it come on?
No broken fuse holders/power sockets etc. (although can be replaced).
Switch in the graphic, pre-shape etc. Does this change the sound.
A normal bass should light the LED by the gain control with it on about three-quarters when played hard.
Most important, can you play it at volume without unwanted/unpleasant distortion? A TE should be able to sound loud and clean.
Don't be alarmed if it has been repaired at some point over the years, this is not unusual.
Understand how a TE amp works, the gain should be set so it flickers on during louder passages. The volume will probably be set fairly low most of the time and still be loud. Pre-shape gives you the 'classic' scooped sound, and isn't as useful as you might expect for many styles. Parametric and graphic EQ work as you would expect.
When I bought my TE 1110 GP11 combo there were a few issues:
Knob missing - sorted thanks to a generous BC member.
Speakers had been replaced, one was wired out of phase. Easy to correct (swap wires over). Some might say the speakers used weren't the best choice, but I never found a problem.
When switched on, all the speakers jumped forwards by an offset (except the out of phase one which moved inwards!) This showed a DC offset caused by a matched pair of transistors going out of spec over the years. I was able to replace these, but if needed you could get a repair shop to do it for you.
There was also another matter related to it being a non-=standard PSU/power amp, but this was not a problem.