Is it possible and easily doable to turn audio into "8-bit"-ish with Sony Vegas Pro 13? Something like 
?
Thanks.
You download the sheet music for the song, then run it through a MIDI app set to old school levels. Basically the days before sampling, audio cards would just give tones. Cakewalk used to be the go to app for this back in the day. It still probably does it with the right settings.
Audio effect wise, try mono PCM with a really low sample rate and the lowest bit depth you can set.
Search online for audio Bitcrusher VST plugin effects. There are loads of freeware ones out there.
iZotope had a free plugin (Vinyl, as I recall) for simulating old or damaged records. Besides the typical pops and ticks setting, it had other degradation parameters that may work.