It is an igniter type ignition and not a CDI. First, quit making assumptions. Start troubleshooting! Make sure there is gas in each bowl by unscrewing the bowl screws and see if gas comes out. If it does, that doesn't mean the carbs are not the problem. It just means you have gas. The carbs can be gunked up and fuel may not be being picked up by the choke circuits or something along those lines but if you have gas, go on to the ignition. First, remove either the #1 or #4 plug and place the electrode right near the engine case. Now turn the bike over with the starter to see if there is spark. If there is, you probably have a tune up issue or lack compression. I would also check with either the 2 or 3 plug. If both have no spark, then check your fuses to ensure none are blown.
At this point, I would buy a multimeter (not a test light). Check for continuity on the fuses rather than using your eyeball as a fuse can be bad without looking blown. Do this by putting the meter on OHMS scale and touching the ends of the fuse with the probes to see if there is coninuity (the element is intact).
If the fuses are good, next check power at your coils. If you put the meter into 20 VDC scale, and put the POS (red) probe on the lug on the coil with the red or yellow red wire and the NEG probe (black one) on the frame and switch the key on, you should have about ~ 12.5 VDC. If you don't have voltage, then you have a simple wiring problem. If you do have voltage, it is time to start troubleshooting the pickup coils (under your point cover) and igniter. Both have specific tests outlined in a factory shop manual. Since these are relatively expensive items, you would be well served to not guess as to what needs replacing. The good news is that both pickup coils and the igniter are used on a zillion Kaw bike models and you can pick up used stuff on eBay reasonably.