Since the fuse doesn't blow now (you did replace it with one of the same ratings, right?), you need to check for:
Replace with one of exactly the same ratings.
If any of these are bad, they will need to be replaced with flameproof resistors of the same ratings (though you can substitute an ordinary resistor for testing purposes). Before applying power, check: Rectifier diodes, horizontal output transistor, regulator pass or chopper transistor (if present), and main filter capacitor for shorts.
An initial test with an ohmmeter can be done while in-circuit. The resistance across each diode and the collector to emitter of the transistors should be relatively high - a few hundred ohms at lest - in at least one direction (in-circuit). If there is a question, unsolder one side of each diode and check - should be in the Megohms or higher in one direction. Removed from the circuit, the collector-emitter resistance should be very high in one direction at least. Depending on the type, the base-emitter resistance may be high in one direction or around 50 ohms. If any reading on a semiconductor device is under 10 ohms - then the device most likely bad. Assuming that you do not have a schematic, you should be able to locate the rectifiers near where the line cord is connected and trace the circuit. The transistors will be either in a TO3 large metal can or a TOP3 plastic package - on heat sinks. The filter capacitor should eventually measure high in one direction (it will take a while to charge from your ohmmeter). It could still be failing at full voltage, however.
If you find one bad part, still check everything else as more than one part may fail and just replacing one may cause it to fail again.
Assuming everything here checks out, clip a voltmeter set on its 500 V scale or higher across the horizontal output transistor and turn the power on. Warning - never measure this point if the horizontal deflection is operating. it is ok now since the set is dead. If the voltage here is 100-150, then there is a problem in the drive to the horizontal output circuit. If it is low or 0, then there are still problems in the power supply or with the winding on the flyback transformer.
Other possible problems: bad hybrid voltage regulator, bad startup circuit, bad standby power supply (dried up filter capacitor, etc.) bad relay contacts as mentioned above. However, these probably would not have blown the fuse in the first place so are less likely.