Let's start with the basics. If your speakers have a power cord check to make sure it is firmly plugged into the electrical outlet. Make sure they are turned on and the volume is turned up. You may (or may not) be suprised by the number of people who discover they have no sound because they did not check the basics.
One thing you can try: are you using on board sound? If so, go to device manager, highlight the sound device, right click and uninstall. Reboot the computer. Windows will see the device as new hardware and install it and the generic windows drivers.
The same thing can be done with a sound card but you will need to install the drivers from the disk that came with the card OR get them from the card manufacturer website. I suggest you look for the card drivers before uninstalling and reinstalling.
If those things are not the problem, then it is possible that the port where the speakers plug into has died.
Do you connect the speakers to the motherboard (on board sound)? If you do and it's dead you have 2 choices
(I'm assuming the system is a desktop because you mention opening the case)
1) replace the motherboard OR
2) purchase a separate sound card and install it. There are some that don't cost very much and are an easy DIY install. A sound card would be the most cost effective option. There is no need to replace the motherboard if its other components are working.
If you already use a separate sound card either plug the speakers into the on board sound (you may have to enable it in BIOS if it doesn't work) OR
replace the card.
edit to add: if you use a sound card did you make sure it is firmly seated when you opened the case?
This is one possible cause for your issue. Someone else may have other ideas to explore.
Edited by Queen-Evie, 30 December 2012 - 03:09 PM.