What you didn't mention was the brand of dishwasher you have. I can't speak for all dishwashers but I've had a similar experience and at least the ones made by Whirlpool (which includes Maytag, KitchenAid, Amana, and some Kenmore) have what is essentially a mini garbage disposal in the bottom. Over the years that grinder accumulates debris that can't be ground and it effects movement of the water through the system. To fix it you have to remove the spray arm mechanism at the bottom at clean out the little sump and screen. There's a bunch of videos out there that show you how to do it, this is one. It's a pretty simple procedure that takes about 15 minutes and a Phillips screwdriver.
If that doesn't do it, you might try a site called "applianceblog" (dot com). It's an online forum for appliace repair and I've used them several times and found their advice spot on. Make sure you include your manufacturer and model number when posting your question.
The age of your dishwasher is the key, while you say its "only" ten years old, by modern standards it's ancient. Most modern dishwashers have a life of 6-8 years, what is most likely happening it the water pump impeller is warn out and not carrying all of the water and food particles away down the drain. There also may be a blockage in your drain line preventing the dishwasher from draining completely.
Try running a cycle with a good dishwasher cleaner such as Finish Dishwasher Cleaner, then run 3-4 cycles with the dishwasher empty to totally flush out the system. If this doesn't solve the problem I would say its time to buy a new dishwasher, as repairs are prohibitively expensive.