How can i get her trust back? was it a big mistake i did on myspace?

I was with my gf for 3months, then i left for Hawaii to work for 4 months. during this period my gf opened my computer & discovered that i have been talking to this girl online (myspace) who was planning on moving to our city. on my 2nd email i gave out my cellphone # & ask her for dinner so i can give her more tips about NYC ( no dates happened). then on my 4th & last email she ask me out to go clubbing but i refused & told her i have a nice gf back home that i love so much. my profile on myspace says i'm in relationship & looking only for friendship. this girl was the one invited me to be her friend. so when my gf found out this inbox in myspace, she freak out & broke up with me. she kicked me out in our apartment last week when i got back from hawaii. and told me she is seeing somebody already. yes when i got home the guy was in our apartment. she accused me of being liar, cheater & betrayal. honestly, i was faithful to my gf the entire relationship even while i was away.