I recently went to start up my 1966 289 V8 after a few months of sitting in the garage. The engine cranked a few times, like when I start it cold, then slowed down then quit cranking and the only thing it would do was spin the starter. The battery is less than 6 months old and appears to be working fine. I first replaced the solenoid since I thought I heard clicking from it and it was quite old. Nothing, still just the starter spinning. Next I replaced the starter. When I took the old one out, it did have some rattling so that gave me hope that it was the culprit. I made sure that I got the correct one for my automatic transmission and installed it. Still the same, only the starter spinning. I guess the next thing would be to check the flywheel? But that is beyond my abilities/know-how. Any suggestions other than tow it to the shop?

 

If you hear the starter spinning, the starter pinion gear is not engaging the flywheel gear. Try jumping with a good battery. If the battery is low it will not throw out the pinion far enough to engage the flywheel ring gear.
No start? Remove the starter and test it with some jumper cables. Negative to housing positive touch to positive cable connection. Put your foot on it as it will have some torque. The solenoid in the starter should kick out the pinion gear, if not bad starter. If slow bad cable , battery or solenoid.
With the starter out look into the starter hole (in the flywheel housing) at the flywheel ring gear. Are the teeth gone? Yes, need new fly wheel gear. Big job.
Try turning over the engine by hand to make sure it is not frozen. However, if this was the case you probably would not hear the starter motor.
My bet bad battery.

 

Well, you were right: bad battery. Now my question is: what is draining the battery? Since I rarely have any time to work on it, I have just disconnected the battery for now; seems like the safest thing to do.

 

Hope you are disconnecting the ground negative side. Always negative first so the wrench doesn't short out to the chasis.
Put an amp meter between the battery and the lead to see how much current is being pulled.
things to check
Bad diodes in alternator, bad regulator cutout, bad headlight switch, bad ignition switch. probably not a short as it would blow a fuse, no aluminum foil around a fuse is there?
Look to see if someone put in a non standard item such as stereo, electric fuel pump or driving lights or automatic radio antenna. Stuff like that.
If high current indicated check the regulator. Also with the engine running check the alternator output. Should be above 13.7 V @ 2200 rpm

 

My first thought is to pull the alternator, since the thought of pulling fuses and testing seems tedious, but that is easier said than done! Bolts on alternator won't budge. Sprayed a few times with WD40 and let them sit. Need to get a breaker bar. There are no aftermarket items. I have the battery completely disconnected right now, so that I can save the charge for testing. I also have no idea where my amp meter is, so I need to get a new one anyway.

 

Be very careful with that long bolt in the alternator. It is prone to break at the first thread in the head. An impact driver might be a better choice over a breaker bar.