Thanks in advance for this

I am sorry i didnt answer you today, i had left my computer on when i went out. 

Cevabim vermediðim sana bugün, özür dilerim.  O zamanda gittim, bilgisayar acikdi.

my try

üzgünüm,bu gün sana bir cevap vermedim,bilgisayarim kapalý deðildi gittiðimde

This works too. I think "üzgünüm" is much stronger than "özer delirim" Its like saying "I am very very upset, that I did that" instead "I (am only) sorry I did that". My opinion.

 Bugün sana cevap vermediðimden özür dilerim, dýþarý gittiðimde bilgisayarýmý açýk býraktým

 Well, üzgünüm states more a ´passive state of mind´ of the person who says it ´he/she feels sad about something´, where as ´özür dilemek´ (to apologize, to beg one´s pardon´, also implies the action of the person who it is said to, as in forgiveness.

I personally would pick özür dilemek, because you want the other to say ´its allright, don´t worry´.

But thats my (non native) opinion

 I think both üzgünüm and özür dilerim are correct, as they are used as synonyms here.. but the idea is, she has left the computer on, and it looked like someone actually was there on the computer, and preferred not to answer.. so to say that, we use -mýþ in the second part, as we didn´t realise that mistake..

Sana cevap vermediðim için üzgünüm / özür dilerim, evden çýkarken bilgisayarý açýk býrakmýþým (that we forgot it on) / býrakmýþtým (we knew that it was on, but we did not realise the consequense).

But I would personally vote on býrakmýþým as it explains why you say sorry...

Oh so much for one line but its great to see the thought process behind it all.

Thanks for taking the time to explain the difference and why.