Mitsubishi Model #CS-40FX1-1993

No the timer circuit would not prevent the Tv from coming on there is logically something else preventing that... The unit is equipped with a shutdown circuit that monitors voltages and prevent it powering up if a certain condition, like a short, is present. Could be the horizontal output transistor is shorted and the shutdown would prevent any B+ from that circuit to prevent a fire. Could be simply that the regulator is shorted and one of the voltages is missing. It's REALLY difficult when the only condition a tech has is that it's dead, or won't power up...
A Mits is a good Tv - really well built. But any good Tv from that era was meant to last about ten years. So when you factor this in your calculations it might just be time to get a new one..
My best suggestion is to take it to a local reputable technician for an estimate. That usually costs something but not an arm and a leg. Then based on what s/he says the problem is and what it will cost to fix it decide whether it's worth it or to replace it with a new Tv...