Take off your engine cover and then the plastic cover over the flywheel and check the postion of your starter bendix (gear that engages the flywheel). If it is up right now, you can rotate it back down using your fingers. Then try your key again to see if it pops back up. If its tight, spray some WD-40 on it and let it sit, then try again. If you are getting this far, then your batteries maybe weak and/or your connections maybe in need of maintenance. Rule this out first since it is simple.
If you batteries check out and the bendix is not stuck, it maybe your starter selenoid or fuse(s). You can check voltages to the selenoid with a VOM. If the selenoid goes, it goes, there is no clicking from your starter, etc. Its just dead. There is a way to test this with a pair of jumper cables and a good battery by jumping the terminals and seeing if the starter will engage. If you have a Clymer manual or equiv. the procedure to test is outlined in there.
If its not the selenoid, batteries or a fuse, try and hand turn the motor in the direction specified on the flywheel, with a large socket and wrench on the flywheel nut. If it turns easily, then I would say its in the electrical system. If it is tight or seized up, then you may have gotten some moisture in the heads causing rust which is too much for your starter to overcome. If its tight, pull the plugs and see if any have rust or a milky/water oil deposit on any of them.
One of our 200's is locked up right now due to what we think is a leaking head gasket. It ran fine last time out then it sat for a month. Took it to the boat ramp. One started, one didn't. After going through all of the above and pulling the plugs, we noticed some rust on two and a milky oil goo on another. We tilted the motor up, filled the cylinders with as much Marvel Mystery Oil as possible, replace the plugs and let it sit for a week. We can at least turn it over now by hand but it is still tight. Going to take the heads off this weekend and have a look inside to see what it up. Hopefully its the gasket(s) and we can hone the cylinders, soak everything in KROIL and get it "restored". Heck of a way to be missing the spring dolphin run.