My iMac will not allow me to log onto my desktop
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.