I was un-cool enough that I wasn't into alternative music at that time. Alternative music, to me, went hand in hand with heroin addiction and we were faux cool...my cohorts were still smoking marijuana but had migrated into cocaine. It didn't mix very well with Punk or New Wave music.
Blondie changed that a little. While many of Debbie Harry's hard core CBGB fans were insulted that they went 'mainstream' with Parallel Lines, this album made punk light accessible to the rest of us, and we loved what we heard. It also caused many people to begin listening to other punk groups, which may have been the end of the punk movement in its heyday.
The album (yes, I had it in disc form back in the day) brought songs like "Heart of Glass", "Hanging on the Telephone" and "One Way or Another" to basic FM radio stations. I always loved listening to Blondie, and listening to her always made me feel a little more naughty than I was.