There should be a factory service manual in the Filebase here on KZR. yellow/gold cover with color wiring diagrams. There's also a poorly copied version floating around the internet, so be sure to get the good one. The diagrams at Partzilla are handy.
I would remove the spark plugs and put a small amount of oil in there or spray some WD-40 into the cylinders. kind of spray around. then reinstall the spark plugs. you could check the gap while they're out. Then remove the RH engine cover. use an impact driver on the engine cover screws (
I use a hand impact driver). remove and service the timing advancer. turn the crankshaft using a 17mmm wrench on the big "nut" to lubricate the cylinder walls. I would go ahead and get a new gasket. I keep several on hand. make sure the engine oil is between the lines at the sight glass.
warning: from the manual. do not use a 14mm wrench on the timing advancer bolt to turn the crankshaft >> doing so could damage the advancer.
New battery. the motorcycle needs a good fully charged battery to start and run right. never assume a battery is good. I use a Ctek US 0.8 smart charger (~$50) and a VC97 digital multimeter (~$30). you could spend less. or more. ha ha.
Drain the fuel tank and carburetors and add fresh fuel. try using the old fuel in a lawn mower mixed w some fresh. You might to need to clean the carburetors. However, before going to all the trouble, you could do the other stuff and see if the motorcycle will start. But if you've never done carb work before, it's not that hard. most stuff is done 4 times. try to return the little parts to the same carburetor, instead of mixing them up. use good fitting tools. you could practice on one carb, remove as much as possible, then reassemble. There may be a simple mechanical synchronization you could do.
Check the air filter and clean out the airbox if necessary.
I would go ahead and change the oil and oil filter. Shell Rotella 15W-40 regular is typically cheaper than other oils. You should at least remove the oil filler cap and sniff for gasoline. you could fashion a dipstick to retrieve a small amount of oil to check it. to see if it's a nice amber color, or black or whatever.
Just a pic under the RH engine cover. the KZ750H Ltd is the same. your advancer should have a different number stamped into it. 1013 I think.