The bottle says it's non-acetone, and I've tried cleaning it up as best as I could. PLEASE give me some advise.I accidentally spilled nail polish remover on my table...help??!!!?
Most likely your table is coated with a lacquer finish. The solvents in the polish remover will soften or even liquefy the finish. DO NOT rub the spill with anything you will remove the finish from the table.
If you are lucky the solvents will evaporate and the finish will re harden, that is the nice thing about lacquer. If after it dries the finish looks bad you can buff out the rough spots.