I've heard this song all over the place, it's called http://www.youtube.com/watch?v=xasb0wXBgXE by Transmissions. Obviously, because of the awkward-as-all-hell-and-ambigious name of the artist/band I cannot find anything else of there's besides the song linked above or some crap about cars.

Could someone please direct me to maybe a YouTube video or two with more material from Transmissions, please?

This should help you out. Google produced this tidbit off their Deus Ex Wikia:

'The song entitled My World was created especially for the campaign by Transmissions, a newly formed Southern California-based duo featuring Susanna Waiche, one of the vocalists for Dirty Projectors, and Kenseth Thibideau from Pinback, among many other bands.'

So try looking up those two bands perhaps?

There's a good chance this band will never make music under this name again. The whole thing was fabricated by an ad agency.

This may be related.

http://grooveshark.com/s/Undone/4duMDP?src=http://forums.bethsoft.com/topic/1498728-need-help-finding-a-music-artist/5