You may need to check that the display is getting separate horizontal and vertical sync pulses. Some setups may use sync on green or other methods.
Is the line horizontal or vertical? Pic handy.
Probably the only other thing to check is the pins at the end of the cable. If any are bent, you MIGHT be able to straighten them again but be careful as they will be weakened already.
Flexing the cable to see if there are any breaks in it may also help to diagnose a bad cable.
Giving the display a good thump on the sides and rear may also prove a dry or cracked solder joint to be the problem. If it briefly alleviates the problem, finding the cracked solder joint can be very tricky.
Other than that, if you need to ask such a question, I'd recommend NOT attempting to open the display. Whilst a Mac Plus is reasonably simple to open and resolder joints, a 17" CRT certainly isn't and there are many dangers lurking inside for the un-initiated.
I imagine there aren't many repair shops around these days that will repair a CRT. Sadly, it became less and less cost effective many years ago, and is no longer a profitable venture