First, I would not try to run the motor until the machine turns freely by hand, too much risk damaging the motor. From pictures I looked at for a White 651 it is likely that the machine is all metal, meaning unless someone took a hammer to it nothing is broken inside (you hope).
I am new here also and have read different approaches to loosening up a stuck machine. Some will us ONLY sewing machine oil, others will loosen with WD40 or the equivalent and then follow up with oil. I have only used oil (OK, I admit I did use a hammer to tap loose a feed dog adjustment rod on a Dressmaker machine, but, well, that was different and the parts were out of the machine) and it just takes time for it to soak in, as in days on one machine I was trying to make move, and it can take multiple applications of oil.
Take off whatever plates or covers you can remove so you can get to metal on metal connections to oil them. Oil is your friend, and I wouldn't rush the job. Once everything is loosened it will go much more quickly.