1st thing to check is your  laser eye,give a clean if not try turning up your laser eye power,other than that  your laser is likely your problem

Line output transformers are very common faults in this make of set,so yes more than likely

You have a convergence problem,a service manual if a novice will  be required

count the number of times it flashs this is a fault code for engineers then you would need repair manual

after power  surges  most equipments power  supplies will  need intensive repairs,flashing led could be a code to what is faulty contact  manufacturer for advise

You will find that there are several (cp`s)) in these units which are circuit protectors most  likely one is open circuit causing loss of voltage 2 motor(these are just fuses but look  like transistors) you might need manual to chase voltage

Try adjusting purity magnets on tube neck

you could have a dry joint on board or screen voltage could need realigned