Welcome to Android Central! How did you delete the contacts? Were they stored locally in the "Phone account," or were they synced with your Google account? If they were only locally stored on the Phone account and you truly deleted them, then you can't get them back, unless you happened to back them up to your computer at some point. If they were synced to your Google account, then they should still be accessible on google.com/contacts.
How do you know it isn't reading all contacts on the SIM card? Are you only unable to add new contacts to the Phone account or SIM card? Can you add a new contact to your Google account?
For this very reason, I always strongly recommend that people associate their contacts with their Google account. They sync automatically, are always available anywhere you have access to a web-enabled computer or device, and act as a foolproof backup.
08-27-2014 07:06 PM