Three flashes to me sounds like 'power supply failure' you did provide a clue
TV takes a while to come on but will come on eventually
a very good clue I say that points to capacitors.
Maybe a power supply repair kit is in order, the only alternative is check all the caps. one by one with an ESR meter, capacitors don't always swell up and get 'huffy puffy' when they are faulty.
You could try and borrow a hair drier from 'Er indoors', slip her a tenner first! Then with the set switched on go round heating the capacitors gently... we are not making toast here so don't get them too warm, maybe finger warm at the most, see what happens.
Dave