From https://sacharts.wordpress.com/2020/08/11/1984-the-facts-and-figures/

1984 saw the start of the UK miners’ strike and that same year the Provisional IRA tried to assassinate Margaret Thatcher by planting a bomb at the Conservative Party’s conference in Brighton. The aids virus was discovered, and the computer game Tetris first appeared. The summer Olympics were held in Los Angeles where local lass Zola Budd (representing Britain) collided with Mary Decker during the 3000m and neither finished the race (And if you want to be a trivia expert, Romania’s Maricica Puica went on to win the race). PW Botha was inaugurated as first State President of SA and news came through of the famine in Ethiopia which led to the Band Aid single and Live Aid concert later that year. Also, the Vatican finally officially forgave Galileo for saying that the earth revolved around the sun (368 years after the event). On the film front a certain Arnold Schwarzenegger appeared in a movie called ‘The Terminator’. The year also saw the births of Calvin Harris, AB de Villiers, Trevor Noah, Olly Murs, Prince Harry, Katie Melua, Dizzee Rascal, Avril Lavigne, Katy Perry and Trey Songz while we said goodbye to Jackie Wilson, Marvin Gaye, Count Basie, Richard Burton, and Truman Capote who all died. The police raided the Stander Gang hideout in Houghton killing gang member Patrick McCall and on the opposite end of the spectrum we sam Desmond Tutu being awarded the Nobel Peace prize.

Based on a points system of 30 points for a number 1 position, 29 for number 2 etc down to 1 for position 30, the following are the top 40 chart performers for the year (Note: this does not necessarily reflect sales):

PosSongArtistPoints
1Clap-Clap SoundKlaxons662
2I Want to Break FreeQueen649
3Red Red WineUB40630
4To All the Girls I’ve Loved BeforeJulio Iglesias600
5Islands in the StreamKenny Rogers590
6Self ControlLaura Branigan573
7Karma ChameleonCulture Club523
8Manuel GoodbyeAudrey Landers519
9FootlooseKenny Loggins454
1099 Red BalloonsNena436
11Happy StationFun Fun433
12Girls Just Want to Have FunCyndi Lauper429
13All Night Long (All Night)Lionel Richie422
14JumpVan Halen418
=15Major TomPeter Schilling406
=15Break My StrideMatthew Wilder406
17What’s Love Got to do with ItTina Turner398
18Dolce VitaRyan Paris388
19Big in JapanAlphaville382
20GhostbustersRay Parker Jr.360
21Sunshine ReggaeLaid Back353
22Dancing in the DarkBruce Springsteen346
23Reggae NightJimmy Cliff344
24Say Say SayPaul McCartney333
25Somebody’s Watching MeRockwell329
=24I Just Called to Say I Love YouStevie Wonder326
=24Love of the Common PeoplePaul Young326
25Colour My LoveFun Fun321
29Radio Ga GaQueen311
30HelloLionel Richie307
31Catch Me (I’m Falling in Love)Marsha Raven306
32Tonight, I Celebrate My LovePeabo Bryson301
33Hold Me NowThompson Twins290
34SusannaArt Company277
35Careless WhisperGeorge Michael272
=36When Doves CryPrince269
-36Boys do Fall in LoveRobin Gibb269
=38Wake Me Up Before You Go-GoWham!265
=38Where is My Man?Eartha Kitt265
40EarthquakeFlirtations260

You can compare this to the list published in Top 40 magazine in 1989 which can be found here:

Top 40 Magazine 1984 List