Note that it *may be* useful to replace a fuse the FIRST time it blows (though it would be better to do some basic checks for shorted components first as there is a small chance that having a fuse blow the second time could result in additional damage which would further complicate the troubleshooting process). However, if the new one blows, there is a real problem and the only use in feeding the TV fuses will be to keep the fuse manufacturer in business!
Sometimes, a fuse will just die of old age or be zapped by a power surge that caused no damage to the rest of the TV. However, it must be an EXACT replacement (including slo-blow if that is what was there originally). Else, there could be safety issues (e.g., fire hazard or equipment damage from too large a current rating) or you could be chasing a non-existent problem (e.g., if the new fuse is not slo-blow and is blown by the degauss circuit inrush current but nothing is actually wrong).
If the fuse really blows absolutely instantly with no indication that the circuits are functioning (no high pitched horizontal deflection whine (if your dog hides under the couch whenever the TV is turned on, deflection is probably working).) then this points to a short somewhere quite near the AC power input. The most common places would be:
You should be able to eliminate these one by one.
Unplug the degauss coil as this will show up as a low resistance.
First, measure across the input to the main power rectifiers - it should not be that low. A reading of only a few ohms may mean a shorted rectifier or two or a shorted Posistor.
If these test good, use an ohmmeter with the set unplugged to measure the horizontal output transistor. Even better to remove it and measure it.
If any readings are under 5 ohms, the transistor is bad. The parts sources listed at the end of this document will have suitable replacements.
If the HOT tests bad, try powering the set first with your light bulb and if it just flashes once when the capacitor is charging, then put a fuse in and try it. The fuse should not blow with the transistor removed.
Of course, not much else will work either.
If it tests good, power the set without the transistor and see what happens. If the fuse does not blow, then with the good transistor (assuming it is not failing under load), it would mean that there is some problem with the driving circuits possibly or with the feedback from the voltages derived from the horizontal not regulating properly.
Look inside the TV and see if you can locate any other large power transistors in metal (TO3) cans or plastic (TOP3) cases. There may be a separate transistor that does the low voltage regulation or a separate regulator IC. Some TVs have a switchmode power supply that runs off a different transistor than the HOT. There is a chance that one of these may be bad. If it is a simple transistor, the same ohmmeter check should be performed.
If none of this proves fruitful, it may be time to try to locate a schematic.
A blown fuse is a very common type of fault due to poor design very often triggered by power surges due to outages or lightning storms. However, the most likely parts to short are easily tested, usually in-circuit, with an ohmmeter and then easily removed to confirm.
If you find the problem and repair it yourself, the cost is likely to be under $25.