This is a long shot, but could it be Goodbye to Winter? It's a student's practice piece from the first volume of the Suzuki Piano method.
It's a nostalgic solo piano song, as per the question. The notes aren't a real match, outside of the (E-D-C riff) but it has the same contour and feel --depending if the rhythm is a match or not.
Located the OST of the film, music credits to Bob Adams / John Kentridge (also at 4:25 into the video).
It is hard to read the image of the back cover of the LP, but the track listing (1b of the Overture, and 6 on side 1) is "Kiss me mother" (trad British Army March) arr. B.Adams.
Some information about the 94th regiment, British army, whose marching tune ...
Based on the linked video's description,
Forever Yours de Wayne Jones
The music is Forever Yours by Wayne Jones.
It's on YouTube and considered as free music.
(Note: the download link is behind ads-powered link-shorteners)
With some help from yahoo answers I found this In-Grid 'Tu es foutu'. Link is to the chorus at the end, which repeats a "turu" sound like the one described.
It is a cool song, so I would like this to be the answer, but you don't give a lot of detail, so there are probably other songs which would fit.
With that in mind:
the yahoo thread above has other ...
The piece is "Concierto para Quinteto" by Astor Piazzolla. There's at least one recording on YouTube by a different ensemble. The audio at your link starts about 3 minutes into the piece. What you heard at the end as "Haciendo Wallace" is actually the announcer starting to announce the name of the piece, "Concierto para...".
Astor Pantaleón Piazzolla (...
Dru Masters wrote the all the music to the series (except for the main theme which is by Sergei Prokofiev). A lot of the music is on the soundtrack album (also available on Amazon). This particular piece is rather featureless, so it's probably not on the album.
The original song as pointed out from Robert Fink is from a bulgarian choir called «Le Mystere de voix Bulgares» and the song is called «Pilentse Pee (Пиленце пее) / Birdie Sings»
Its the first track of this album on YouTube:
Le Mystere de voix Bulgares - Birdie Sings
This is a circle of fifths progression --one of the most common of all chord progressions in both classical and popular music.
It comes up particularly often in Bach --for instance, here in the Brandenburg Concerto No. 2 in F major, BWV 1047, I. Allegro.