Scandinavian synth-poppy band from the 80s and it isn’t A-ha? Damn. 
The band might be ABECEDARIANS. Did she go to college in Los Angeles, CA? ABECEDARIANS were a big deal in the late 80s with the college folks in LA. They had a great song called Wildflowers Grow From The Trash.
New Haven, CT actually.
I know the band was European, kind of alpaville-y. Maybe it was alphaville.
I seem to recall thinking that the Alphaville song ‘Forever Young’ was by the Cure. But I’m guessing that nobody would confuse the Cure with Alphaville. The Cure was much bigger by that time. Otherwise I’ve got nothing.
Associates?
The band I always got confused with Alphaville was Cutting Crew.
Could it be Lupus?
Army of Lovers?
A, Swedish, formed in late 80s, dancey.
Yaz?
Oh!!!
Maybe that is it - it was Alphaville and I always confused them with Cutting Crew!!
Going to investigate a bit. This might be it!
It’s never Lupus.
I’m glad that the connection was made, because Cutting Crew sounds more like 80s AOR than synth pop, at least to my ears. 
They’re British, btw. I used to get them mixed up with Johnny Hates Jazz and The Rembrandts. Musically I think they sound like Naked Eyes and Wang Chung a bit (who predate them somewhat).
OK, to recap.
I am almost positive now that the story really goes:
"My sister went away to college in 1986, and discovered a band that I can’t remember the name of. It would have been a band currently putting out music in 1986, but I don’t know if 1986 was near the beginning, middle or end of their career.
I used the get them mixed up with CUTTING CREW, which annoyed my sister. I am almost 100% sure their name began with A. They were probably kind of synth-poppy and soft. Maybe some variety of Scandinavian?"
Maybe this is my chance to ask a mod to change a thread title.
Long Shot - Identify this band from the 80s who was [actually really] Alphaville?
Huh. And I was thinking maybe Erasure.
Air Supply?
Despite your recollection, I still say it was Falco.
I am with **conway **on this. Everything in music from 1980 to about 1987 was Falco under different names.
Remember when he changed it to Taco? He wasn’t even trying.
Coming in with a longshot with Blancmange.