My iMac will not allow me to log onto my desktop I got a viruses alert when using my Mac and sadly I reacted ASAP.

I gave control to a remote technican via log-me-in and I went through the steps that where asked. After I got off the phone with the supposedly technicians I decided to change my desktop passwords using my old password and to create a new one and it bargain to say my old one was incorrect so I called back they said for me to shut it down so I did and I haven't been able to log back in to my desk top computer at all. 

Is there anyway I could unlock and access my computer back like be for with out damaging orlosing any files?
I agree with bmike that since we don't know what the nefarious people have done to you, it's next to impossible to diagnose the problem here.

However, I am going on the premise that you can turn on your computer but you just cannot log in - meaning enter your username/password - as you described.

To reset your OS X password without installation media you need to start up in single user mode via the terminal and create a new Admin account:


Reboot/turn on your comptuer
Hold Command + S while turning on until after you hear the chime.
When you get a text prompt enter in these terminal commands to create a brand new admin account (hitting return after each line):


mount -uw /

rm /var/db/.AppleSetupDone

shutdown -h now

After restarting your iMac you should have a new Admin account. When you login as the new Admin you just delete old one, reset your other accounts (if any) and you should be good to go.

Once you get to this step, I highly...and I mean highly like this is a moral imperative...recommend that you change all the passwords for the services that you have stored in your Keychain.  

Let us know how you make out.