It may well be that in your case only a minor component of the sound system (mainly ALSA and pulseaudio) is missing that could be reinstalled or reconfigured easily. To tell this you should exactly know what you have done, what you have removed and what you may have installed as a replacement. From what you write in your question this unfortunately seems not to be the case.
What to do if we removed all or part of the sound system?
Restoring the sound system would in theory be possible by reinstalling all sound related packages including their default system wide settings, but to my experience a fresh install of Ubuntu is much faster, safer, and easier. Take care to keep your settings and data in your /home directory untouched. You may have to reinstall some additional packages but you will see that even these will have kept your individual settings from your untouched /home.
Is it only a wrong user setting?
If you only changed settings and configuration files but did not remove packages there may indeed be a good chance to recover your system. You can easily find out if your sound problems come from a wrong user setting or from system wide settings by looking at sound in the guest account or by creating a new user account. In case this new user has sound you will find all default settings in the new user's /home. In some cases wrong pulseaudio settings in a user's home can be removed by renaming/deleting
~/.pulse in older releases).
mv ~/.config/pulse ~/.config/pulse.old
Of course this will not help when system-wide settings are broken.