You should never save the file with its contents starting with -----BEGIN RSA PRIVATE KEY----- on the server, that is your private key. Instead, you must put the public key into the ~/.ssh/authorized_keys file.

This public key has the .pub extension when generated using ssh-keygen and its contents begin with ssh-rsa AAAAB3. (The binary format is described in the answers to this question).

The permissions of ~/.ssh on the server should be 700. The file ~/.ssh/authorized_keys (on the server) is supposed to have a mode of 600. The permissions of the (private) key on the client-side should be 600.

If the private key was not protected with a password, and you put it on the server, I recommend you to generate a new one:

ssh-keygen -t rsa

You can skip this if you're fully sure that nobody can recover the deleted private key from the server.

If this does not help, run ssh with options for more verbosity:

ssh -vvv user@example.com

On the server side, you can review /var/log/auth.log for details.