So I just purchased a 2000 Suzuki Katana 600. The bike cranks but doesn't want to start. I had the battery tested and it was good. I can get it started with some starter fluid. Then if I go ride it or it sits for any amount of time I have the same issue. It cranks over but it sounds like it's really struggling to do so then after continuously trying it stops cranking. So it sounds like a battery but was told it was good. Any help would be greatly appreciated.
Always start with the basics. To run an gasoline internal combustion engine requires:
First of all this bike has carburetors and these can be very sensitive to storage especially with ethanol-laced fuels. From your description that it starts on starter fluid indicate problems with fueling. You'll probably want to rebuild the carbs to resolve this issue. There are some in-fuel carb cleaning products but I've had little success with any of them. But they are relatively inexpensive and easy to use so it's probably worth a try. Also check that the choke or cold-start enriching circuit and its control is working properly.
Check your airbox and air cleaner to be sure nothing has built a nest in there and the filter is clean.
A compression test is simple enough to do and will give you an indication of the health of the piston rings and valves. These types of engines will run on 3 out of 4 cylinders but not well and can be difficult to start.
It sounds like your ignition, i.e. spark plugs and coils are working OK. So I'd leave those go for now.