The Important of Oscilloscope
Under normal troubleshooting and repair i do not use oscilloscope. I will only use scope when i want to measure the waveform output from the IC. Assuming there is a one horizontal line across the screen of the Monitor and you have checked the surrounding components at the vertical IC and even replaced the vertical IC and still could not find the fault. In this situation i will use scope to test if there is any missing signal from the vertical oscillator IC. Most of the time by using oscilloscope to troubleshoot electronic equipment, chances are very high that i could repair the problem.
If you do not have a scope i strongly suggest you to invest one to speed up your troubleshooting and save massive amount of time. Nowadays scope are quite cheap especially if you have the opportunity to buy over the scope from the electronic related factories that wanted to close their operation or move to other countries. I have a friend who bought a working 100MHZ scope for less than US100+!