Most likely the feed dogs just need oil to get unstuck. Sometimes the oil has to sit for quite awhile in order to penetrate.
Even if the feed dogs never drop, you can probably still use the machine for FMQ. You can set stitch length to 0 and leave the feed dogs up; some quilters prefer it that way! Or, you can make a plastic cover for the feed dogs to tape in place. Some machines have feed dog covers for this purpose; a homemade feed dog cover can work just as well.