Sewing machine oil inside and out. Wipe it down with some sewing machine oil. Other oils are too heavy or can gum up or both. If it has plastic gears, no oil on those. Some plastics are sensitive to oil and can be damaged by it.
Take the top off and oil everything that is metal and looks like it should move. Do the same to the bottom and inside the nose. Take the bobbin and bobbin case out. Most machines it's easy to remove the hook too and a lot of times you will find a thread jam behind there making things stick.
With a little time and patience you'll get it freed up. Try gently rocking the wheel back and forth. Any movement is good and will help the oil soak in. It didn't freeze up overnight, you can expect it to take some time to get unstuck.
Rodney

Dead on, Rodney. Could it have a broken gear inside?

I couldn't say without looking. It's possible but most likely it's just stuck from dried oil and sitting. My experience with the two I have that have broken gears is one the gear disintegrated when it let go so the top half turns freely and the bottom doesn't move. The other one has a cracked hook drive gear and that one will turn but hangs up at the crack.
That machine looks old enough I'm guessing it's all metal inside so the chances of a broken gear are smaller.
Rodney

Ok I looked back up there - I doubt if it has a broken gear. If the clutch is engaged and it doesn't turn there no doubt is some dried up oil in a shaft somewhere. It can take time for the oil to work it's way into the shaft and get it to free up. Sometimes heat helps move the oil into the cracks. I'm thinking judging by the body look of the machine that it was made by Brother. Some times you can tell by the stampings under the machine. You might be able to get an owner's manual by contacting Brother hhmmm maybe it was Janome... Anyway some times you can get manuals from the manufacture.

That one I'm not even going to guess who made it. I think if it was Brother Cari would be in here too. I did see the same machine recently on Portland's Craig's List IIRC.
I own a couple Remingtons but not sewing machines.
Rodney

I've seen a couple Remingtons built by Brother but I don't think this one is. Nothing about it screams Brother to me. It is a cool looking machine though and I think you're right about getting it to free up. Though I'd get the top off of it and start with rubbing alcohol.

Cari

If Rubbing Alcohol is used Care has to be taken that it does not get on the paint. It will damage it.
~Grant~

Good call Grant, I should have been more specific. I would clean the insides of the machine with alcohol to start the freeing up process, then use sewing machine oil.

Cari

I do use Rubbing Alcohol on certain things. I put it on a Q-Tip to control where it goes. I got some wood handled ones like you see in medical offices. They are 6" long and hold up better than paper ones.
On gears, a wire bush is quite useful. Metal gears need grease. Just about everything else needs oil. Oil where you see two metal parts moving in a joint. Also in any oil holes. They don't have screw threads inside of them. Wipe off the excess. If you can find Tri-Flow oil, it is the best IMHO. It works faster on seized up machines than Singer oil.
Those are nice looking machines Maria and Missykay. It makes me feel good to know someone is giving them both some love. :thumbup:
~Grant~

Ok...Thank you. I was trying to find some gears that may be locked up, but I don't know where there would be any on the underside. Should I take that faceplate off? The screws are really tight and I don't want to risk breaking or stripping them. The top is really in good shape, there's not a lot of dust in there so I'm pretty sure that its locked up on the underside. [ATTACH=CONFIG]494582[/ATTACH]