Clean them well and change the hardware. Use Murphy's Oil soap on the wooden trim. Without seeing the entire space, or knowing what your tastes are, it is hard to make recommendations to update the space but, as you see, painting didn't work so I would leave the cabinets alone.

have to see more what the space is like. try a skinny simple stainless pull . should be standard center to center dimension so easy to substitute a cleaner look for hardware. Just keep doing what you are doing. looks like maybe new counters could enhance things but again more images always help with creative ideas. you are doing great. some of those cabinets are more enduring and almost "classic" than others. I've seen some of that type that almost fall apart and some so super rugged/ great construction and thicker materials so they've held up amazing over 40 yrs or so.

Thanks a lot for the comments!! A lot needs changing in this kitchen. In the near future we will be tearing it down and expanding into the dining room. Big project for sure. We may go with just painting the wood part white so it does not look too outdated. Then use some new black hardware. Thanks again for the advice!!!!

the wood looks good .very rich I would not paint it. that would be a shame.

That was my thought initially, but my husband says it is moldy inside. Can you suggest a fix for that?

moldy inside where? no sign of that from what I see

See the black spots? Not sure how to fix it, or if trying to fix it would be worth it for just a couple of years.

tannins in wood react and cause black spots. if you have WOODCRAFT store near you take a drawer front in. there are some products to remove but being along the edge like that rather than a big flat area makes application a little different. they may have a process that would work well however. I doubt its mold. but the nature of your goal and so on...I think I might gel stain a darker color after a bit of exploring about the spots but not to drive myself crazy. painting doesnt appeal to me along there...have you ever gel stained ? that would be kind of a nice spot for it but i've done a bit of it . if you just go darker like a deeper chestnut you just get a saturated look and might wear better than paint there. GOOD LUCK.

Excellent advice! Will look into gel staining.