Cleaning and polishing furniture - what to use?

[Alibear1]

I have inherited a lovely sideboard from my grandparents, we've had it for 2 years and I've never done anything other than dust it. It's in good condition, no scratches etc, but it's a bit grubby around where the handles are for the doors and the drawers. I got some furniture polish and I've had a go with it this morning but it doesn't seem to be lifting the dirt off very well, although the wood does look better and feels less dry to the touch.
Is there some amazing product out there that anyone can share with me or do I just need to keep plugging away with the polish? I'm wary of using anything too strong as I don't want to damage it.

All tips gratefully received!

[PuzzleRocks]

Bumping for you.

[Alibear1]

Bump - anyone?

[nontoxic]

I'd probably have a go with a white vinegar solution - or even use it neat. The grubby marks are probably where polish has built up and dust has settled in.

Vinegar (distilled) is fine on wood, and the pong fades quickly.

[Fimbo]

Try Bicarb - here for the handles etc