Hi Marcus,
Keyboards are always a sticky issue, since that's where all the dirt and liquids end up when they're loosened upon the world as you're working on your computer.
Best thing you can try is to turn off the computer and remove the battery, then remove the key caps and the hinges and rubber pieces and clean it out with high concentration (90% or better) isopropyl alcohol. Blow or vacuum it well then reassemble and test.
That's really about all you can do; if that doesn't fix the issue then you're probably going to have to replace the keyboard. Naturally it's not that easy; the keyboard, upper case and trackpad all come as a single unit which makes replacement easier but costs more. Fortunately those systems are old enough that replacement parts are easy to find and getting more inexpensive all the time. Check Amazon, eBay and AliExpress for your specific model number.
The upper case itself isn't too bad to replace, and iFixit has a guide to step you through the whole process.
[guide|515|MacBook Core 2 Duo Upper Case Replacement - iFixit Repair Guide|new_window=true]
Good luck with it; let us know what you find and how it turns out!