You haven't really given enough information about your style and what you like to really give you a great suggestion on what to do with your outdated kitchen but this is what you may consider.
Instead of painting the backsplash, you may consider trying some kind of tin or metal plating application to the backsplash instead. They come in different colors and textures and would really lend some great pop to that area.
While you don't have any natural light, it doesn't necessarily equal a dark kitchen. How much lighting do you have in your kitchen? Since your husband is against painting the cabinets perhaps he would be willing to sand and restain them (remember no matter what you do to get new hardware (hinges and knobs) for the cabinets). If you are going to keep that color cabinet, you need to determine if you want them to stand out or blend in. Some colors that would work well with those cabinets their pine color would be yellows, oranges, or greens. If you wanted them to pop, blues or whites or browns would be able to do that for you.
I personally would love to see some kind of bright orange (like a tomato) or yellow (like a yellow pepper or lemon) or even a touch of green (like grass or peas) in there for a dramatic difference. If you wouldn't want the drama, go for a lighter version of these colors.
The metal or metal looking wall tiles I'm talking about come in 18"x18" or 24"x24" squares and fasten to the wall easily. You can find them at Lowes or HomeDepot. and they are very easy to measure and cut even with the pattern.
I would also suggest putting some tap lights under the cabinets to light the countertop. This adds a very nice feel to the kitchen work area. Don't be afraid to think and go outside the box. Paint is cheap and can be painted over. I tend to stay away from oil based paints because I don't like working with the oil based paint's paint removers.