There was a sudden lost of power in my house, so my computer immediately turned off while it was playing a song, but then I rebooted it, there's no more sounds coming out of my computer, why is it like that? and yes I tested out my speaker to my laptop and it is working, I also checked the device manager my audio card is installed, why is it like this? how would I fix this?
I assume both your computer and your speakers lost power. Both may have been damaged.
So you know that the speakers are fine and the problem is with the computer.
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.
If you have a real audio card:
If by audio card you mean the audio parts build into the motherboard: