Festival: Don't Cry For Me Argentina
I don't remember this one, THANK GOD!
YMO: Computer Game
Yes I remember this one, Ryuichia Sakamoto's futuristic pop band.  "Computer Game," not to be confused with the Aussie group Mi-Sex and there hit from the same year, "Computer Games," which is a cool New Wave song.
The Tourists: I Only Want to Be With You
The tourists were the band Annie Lennox and Dave Stewart were in before forming Eurythmics.  So their records should have been great, right?  Nah.  I thought they were rather bland.
The Afternoon Delights: General Hosp-itale
I wished this song was a lot MORE minor!  Chr*st, it was annoying!  For several seasons "General Hospital" was all the rage, especially in re: the whole "Luke and Laura" thing.  Deft marketing blinded people to the fact that GH was just another inane soap opera.  My sister was all wrapped up in that soap for about fifteen years.  Bleccchhh!
Tight Fit: Back to the '60s
Uhhhh.....what?
The Spys: Don't Run My Life
Hum the tune, maybe I'll remember.
The Stompers: Never Tell An Angel When Your Heart's On Fire
This was a pretty big hit in the Boston area as the Stompers played every club, every festival, every county fair, every wedding, every bar mitzvah, and every sewage treatment plant grand opening for about a decade.  They were the epitome of sub-par townie-yahoo Boston rock.  Yeesh!
Charlie: It's Inevitable
In 1983 I listened to ATF with Casey Kasem every week, so I remember this exceedingly dull rock'n'roll song by dint of it making the Billboard top 40 for about three weeks.
FR David: Words
Don't remember it.  If it made it to no. 40, I would!
Moroder/Engemannn: Reach Out (Olympics theme)
Ubiquitous early '80s schlock of Giorgie Moroder, why must the show go on?
Roger Hodgson: Had A Dream (Sleeping With the Enemy)
A guilty pleasure.  Considering how much I despise Supertramp, a very guilty pleasure indeed!
:-Yes, from Billy's album, "Mahvelous."  Billy exploited Fernando to the fullest.  Fernando even pitched for Pepsi in 1984.  I couldn't figure out who was more shameless, Billy or Fernando!  The video was quite funny though.  "I love you kids today, with your rock'n'roll, like that Eddie Van Heflen..."
"VAN HALEN"
"...Whaddever."
Menudo: Hold Me
No comment.
Urgent: Running Back
Was that one of those football songs?
King: Love & Pride
Not a very good band, but I always loved this song.  I still listen to it now and again.  The video was cool with the guy spray painting everywhere.  Very '80s dance rhythm.
Murray Head: One Night in Bankok
I don't know about "Robey," I always saw it credited to Murray Head, and I remember the video with said actor.  His name wasn't "Head" for nothin.'  Anyway, the song was from the musical "Chess," I think it was written by Tim Rice.  "Tea girls, small and sweet, some are set up in the Somerset Maugham suite/Get tied, you're talking to a tourist whose every move's among the purist..."  Another guilty pleasure, very cheesy indeed!
Wax: Right Between the Eyes
Might recall it if I heard it
Rock and Hyde: Dirty Water
Can't say I remember this version, though I remember the Tin Huey version, and of course the original by Tommy James and the Shondells, a perennial fave around Boston.  "Love that dirty water, Ohhh, Boston, you're my home!"
The Time Lords: Doctorin' the Tardis
Strong sense memory of this song, listening to it lying in bed, waiting for my Gothy girlfriend to finish taking off her makeup
1927: That's When I Think of You
? ? ? ?

OK, well, I'll go back and listen to the clips of the ones I don't remember. 
And I'll add one, if I may
Dragon: Rain (U.S. #88)
This old Aussie band revamped themselves for an '80s hit, and they did a great job.  I remember it getting a lot of airplay for a song that only reached 88.  The thing is, I didn't the single or the album ("Body and the Beat"), both of which went out of print in a big hurry.  I looked for this song for years and years.  Finally, I found the album online and bought it.  I liked the song as much 1999 as in 1984.  The rest of the album was thoroughly mediocre.

I don't know about "Robey," I always saw it credited to Murray Head, and I remember the video with said actor.  His name wasn't "Head" for nothin.'  Anyway, the song was from the musical "Chess," I think it was written by Tim Rice.  "Tea girls, small and sweet, some are set up in the Somerset Maugham suite/Get tied, you're talking to a tourist whose every move's among the purist..."  Another guilty pleasure, very cheesy indeed!

Robey's version was a cover and it charted just 1 week after Murray's original hit the top 20.  I like Murray's original much better

http://image.com.com/mp3/images/cover/200/drd300/d360/d360527j8je.jpg

The Spys: Don't Run My Life
Hum the tune, maybe I'll remember.

The Spys were a product of Ed Gagliardi and Al Greenwood, ex-founding members of Foreigner.  Don't Run My Life was a top 20 hit here in Canada, a very minor hit in America, and it remained their only hit

http://images.amazon.com/images/P/B000005NN2.01._SCLZZZZZZZ_.jpg

OK, OK, now I remember both Robey and the Spys.  Thanks for the visuals.

Reach Out :Track Theme For the Los Angeles 1984 Olympiad- Giorgio Moroder featuring Paul Engemann
  My father worked for Ford Motor Corp as a Technician for 20+ years and Ford made this cassette for new cars (in 84)...so customers had something to play on the way home assuming you didn't bring a tape to the dealer to buy the car. Anyhow, this was one song and it is so inspiring, you can visualize the runners holding a torch and the flags flying. Aaah: the emotions!

Love and Pride - King
I agree with others. I did like this song immensely and still do. I think I only remember one other song by King tho.