I have audio available (recorded or I can sing/play it)
Musipedia (hum, enter notation, or enter pitch "contour" [i.e., up, down, repeat])
A searchable, editable, and expandable collection of tunes, melodies, and musical themes. (Musipedia)
Shazam (uses 10-second clip of song)
The application can identify music, movies, advertising, and ...
The piece playing from 17:26 to 19:27 in Chopin's Prelude in D Minor, op. 28 no. 4.
The entire video incorporates Chopin's music.
4:30 - 6:45: Prelude in A Flat Major, op. 28 no. 17
6:51 - 7:40: Prelude in C Major, op. 28 no. 1
8:42 - 10:30: Prelude in G Major, op. 28 no. 2
12:10 - 13:10: Prelude in C Sharp Minor, op. 28 no. 10
14:15 - 15:25: Prelude in B ...
Here's a long shot: Summerlong by Emm Gryner.
Released in 1998, it was on the radio a lot that summer in Canada.
Female voice, but solo act not a group.
Speed isn't terribly slow but it is melodic.
Chorus contains "Summerlong" which has the syllable structure as the potentially remembered words.
Emm Gryner hasn't reached super-popularity although ...
The Story, "Grace in Gravity" (Cranberries-ish)
Celine Dion, "My Heart Will Go On" ("Wherever" + #1 in Italy, 28 Feb - 14 Mar 1998)
There are lists of the Italian weekly top 20 here (hitparadeitalia.it).
You also could look through the "map" of "if you like the Cranberries, you might also like...&...
You may find this book helpful:
Annala, Hannu, and Heiki Mätlik. 2007. Handbook of guitar and lute composers. Pacific, MO: Mel Bay.
It appears to be available as an ebook, which would facilitate searching. A quick search via Google books turned up both Boccherini (as expected, based on PiedPiper's answer) and also a guitar with string quintet (and ...
The song is "Devotion" by Hurts, featuring Kylie Minogue. It sounds like the version you posted has been slowed down and pitch lowered. Possibly a Nightcore version.
Here's the closest I've found. It lacks the industrial noise at the beginning.
You Light Up My Life originally by Kasy Cisyk (1977) but best known by Debby Boone was released in 1977, so was I...so it's a 42 year old song.
Others have done remakes like LeAnn Rimes (1997), Yuki Saito (1994), and Whitney Houston (2002). There were also male vocalists released but you said it was female. Hope that helped.