Windows 7 no sound coming out of the speaker

Solution 1:

There was a sudden lost of power in my house, so my computer immediately turned off.

I assume both your computer and your speakers lost power. Both may have been damaged.

There is no more sounds coming out of my computer. I tested my speakers with my laptop and it is working.

So you know that the speakers are fine and the problem is with the computer.

I checked the device manager; my audio card is installed.

If there is a sudden loss of power (e.g. due to a black out or a blown fuse) you may get spikes on your power grid. Things are likely to break when that happens, and that includes computers. Both their PSU, the motherboard and cards plugged into the motherboard. Sometimes they fail completely. Sometimes they fail partially. The audio part is not the first thing I expect to fail, but since the speakers where also plugged in at the same moment it may have sent a spike to the audio out part of your computer.

how would I fix this?

If you have a real audio card:
Remove it. Check for black marks. Test it in another computer.

If by audio card you mean the audio parts build into the motherboard:

• Check for black (burn) marks.
• Try a liveCD or a fresh installation to make sure it is a hardware and not a software problem.
• Replace motherboard.