I used to own a 336C in 35 remington and the lever action was tighter side to side than winchester 94s that I own. As others have said, make sure the barrel and chamber are clear, everything is tight and give it a run. The old "JM" stamped Marlins are some tuff, well built guns, not like the Remlins we see today.
Clean it then enjoy it, they tend to be accurate have shot quite a few of them over the years, seem to be well made at least back in the early 70's they were good rifles. If you don't feel comfy doing that, then stop by a gunsmith and have it checked out. ;-) To the OP yes if the action cycles fine & the bore clean I would take the rifle out to shoot it. If it all feels tight, I'd giver' a good cleaning and send one down range.
I still use it depending on the terrain I'm hunting in.
Here Kitty Kitty I have a 336 in .35Rem that was made in the '40's..a sweet action.
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I have in my collection that I purchased the other day a 336 Marlin 30-30 and the stock is pretty beat up and the guy that sold me the gun had NEVER FIRED it .
So I was a little hesitant on buying it but what struck me as odd was the lever action on this was like brand new not sloppy and the feeder tube were you load it wasn't worn down from shoving shells into it and just by looking at it could tell it hasn't been re-blued . is should I just put a round into her and pull the trigger and see what happens or should I do the right thing and seek out a gunsmith .
The early Model 1895 rifles were chambered for a variety of 45-70 cartridges: 45-70 Gov't, 45-70 Marlin, 45-70 WCF, 45-70-330 Gould Express, and 45 Gov't Short Range.
I presently own 28 different calibers and 32 rifles.