Cabinets, Sticky Finish

[Donald Crockett]

I think this is my first post other than my intro post.

We're getting a house we just bought ready to rent. The kitchen cabinets are structurally sound and they look great however the people who had lived there apparently didn't use the handles on the doors and drawers. They just grabbed the edges of the doors and drawers to open and close. Now, anywhere hands have been touching the varnish is very sticky and tacky. We've tried various cleaning methods from gentle to severe with no luck, It is actually the varnish that is soft and almost gummy. So as I see it, options are replacement (which we'd like to avoid if possible), re-facing with new doors and drawer fronts, or striping and refinishing.

My question is, is there any way to solve this issue other than the remedies I've mentioned? The cabinets really look great, they're up to date in appearance, and they're of fairly good quality. I'd hate to scrap them. Any advice?