If your front panel has two inputs like mine, I would consider plugging the speakers into the first and the headphones into the other. Microphone goes in the back. Just configure everything and make sure it works.
Drivers should allow you to point what type of device you've connected for each input.
If you have 1 front input only you're... not lucky.
I'm not really your hardware guy, last thing I'd suggest is a soundcard refresh:
1. Go to the start menu and type "Device Manager".
2. Click the arrow next to "Sound, video and game controllers".
3. Find your audiocard in the list, it should be something like "DP965LT Mobo", as you pointed out.
4. Right click your audiocard and say "Disable".
5. Restart the computer.
6. Go to "Device Manager" again and repeat steps 2 and 3.
7. This time, right click and select "Enable".
8. Test your audio again, if the problem persists, try a second computer reboot.
9. Test everything again.
10. If the problem
still persists, read the part before the comma in the 6th sentence in my post. (The one after "If you have 1 front input only you're... not lucky.")