Hi, Thenia. The general process to do this right is to strip any film finish, bleach the wood probably with household bleach or oxalic acid,restain and refinish. This will be a big project and very messy. It is no different than doing it on furniture or moldings or kitchen cabinets. The cost will add up but should still be less than replacement. If you will look down this board and at www.citristrip.com , I have posted a lot of info on the process.
You could try a light sanding with 150 grit paper just to give the surface some tooth and then paint on a Minwax pastel stain color and wipe it mostly back off. No guarantee that this will work as a lot depends on your paneling and the finish on it. Try a small section in an out of the way location and wash the stain off with mineral spirits/paint thinner if it obviously isn't working or giving you the results you want. Even better would be to run your tests on any leftover sections of the paneling, but you probably don't have any.