Delta Goodrem - Lost Without You
No Doubt - Running
Nelly Furtado - Try
Jem - Falling For You
Jem - Missing You


these songs got released 1 or 2 years before 2004.. hop you don't mind :P
but you really should check them out if you don't know them :yes

I'll look through my music collection. :)
English only, let's see...

Kryptonite - 3 Doors Down (it was released in 2004 though..).
She Will Love You - Aiden (I like it anyway! XD).
Dance Inside - The All-American Rejects
When You're Gone - Avril Lavigne
Hot - Avril Lavigne
Hands Down - Dashboard Confessional (was released in 2003...but it's really sweet).
Emily - From First to Last (very different from their usual stuff which I mostly dislike! :))
December Love Song - Gackt (if you can deal with engrish :))
Polaris - Jimmy Eat World
Blue and Yellow - The Used (2002...)
Noise and Kisses - The Used (2002 also, and a little strange, but I love it!)

Ehh...that's all I can think of. :P
I'm sorry if some of the songs are in genres you don't like! :P

OMG this song always makes me feel relaxed and makes me think of my best friend who i love so much
XP

Foo Fighters - Everlong

Natasha Beddingfield - soulmate its a sad love song though, really sad :(

some others:

Ashlee Simpson - L.O.V.E
Christina Milian - my lovin' goes
Plain White T's - hey there delilah
Leona Lewis - Angel (this song is BEAUTIFUL!! you should really listen to it :luv2)