Do you know how to remove the bolt from the gun? Check to make sure there is no round in it. Close the bolt, pull the trigger and hold it back. While holding the trigger, lift the bolt handle up and back. Should pull right out the back.
I would soak the bolt in a solvent. consider buying an empty paint can from home depot, pouring in a little bit of kerosene and letting the bolt soak for a few hours.
While letting it soak go back to the bolt-less action and stock. Give the barrel a good cleaning. I would start buy running a couple cleaning patches with cleaner on them through it first. Then run a cleaning rod with a .22 wire brush on it through the back where the bolt came out of into barrel chamber and out the muzzle in one direction. Do this a couple more times. Run another cleaning patches with cleaner on through it, then a couple dry patches.
Next I would inspect the inside of the barrel. The gun should be empty with the bolt removed, so it is safe to look down the barrel. Take a flashlight and put it up to where the bolt was removed and shine it down the barrel. Look down the barrel. Hopefully you see smooth surface with visible rifling.
I would take the stock off the action and barrel. This is done by removing two screws on the underside of the stock and lifting the action out the top. Clean every nook and cranny you can. q-tips are your friend.
After clean. Put the stock back on the action. Tighten screws to an even snugness. To put bolt back in, squeeze trigger with safety off and slide the bolt back in after putting a light coat of oil on it.
These people sell the magazine you are looking for.
http://www.ammoclip.com/m/marlin_80,80c,80dl,80e.htm