It's either the screen itself, the cable, or even the motherboard. The first step is making sure it doesn't do the same thing on an external display. If it does, then it's definitely a motherboard. If it doesn't, then my next step would be to take the bottom off and re-seat the screen cable to the motherboard, just because this is the next easiest thing to do. If that doesn't fix the problem, you need to disassemble the display assembly and connect a testing screen. Make sure it has the same connection (30 or 40 pin) and resolution. It doesn't matter if it's a 14", 15" or 17" screen so long as the connection type and resolution match. If it does it on the testing screen then it's time to buy a replacement cable. There's still a chance that the problem is with the motherboard but the only way to test it is by replacing the cable.
Oh, and also test the existing screen once you've got it out of the display assembly. If it only happens when it's inside of the assembly, then gently flex and put pressure on the screen to make sure it's actually the screen that's bad. You might notice that jiggling the cable or flexing the screen near the bottom board where the cable attaches causes the screen to flicker. If that happens then try the same thing with your testing screen attached. If it happens with both screens then it's definitely a cable issue.
This is why it's important to charge a good amount for diagnostics, especially nowadays. Not only do you weed out the people who aren't serious about getting their computer fixed, but you can occasionally spend a few hours diagnosing a computer if necessary.
Be honest to the client that it's a process of elimination and that you can't guarantee a fix, but give them an appropriate percentage chance that it gets fixed if you buy a new screen or a new cable or whatever. I have a no fix no pay policy, but it only applies if they decide to trade it in and buy a computer from me instead. So for example if I replaced the cable and it didn't fix the problem, I'd let them know that we need to replace the motherboard instead and that they won't be charged for the cable replacement. If they decided that they didn't want to wait for the repair any longer, I'd put 100% of what I would have charged them for the work that I'd already done (minus the diagnostic) towards another computer. So if I quoted them $75 for a diagnostic and $329 to replace the cable and it didn't work, they're only in it for the $75 so long as they choose to fix what the problem actually is with the computer OR decide to trade it in and buy something else from me.