Unable to re-install Gravity Forms after domain transfer

We recently transferred our domain name to our WordPress web site. The transfer has completed successfully; however, we appear to no longer have the same connections with WordPress, including Gravity Forms. This morning I tried to run a plugin update for Gravity Forms, and now we no longer have them in our Dashboard at all. We cannot re-install Gravity Forms either and receive this message:
Unpacking the package…
Installing the plugin…
Destination folder already exists. /var/www/vhosts/03568AF.NETSOLVPS.COM/httpdocs/wordpress/wp-content/plugins/gravityforms/
Plugin install failed.
I really think this is an issue with connection to our WordPress database. Does anyone know how we can re-establish our connection in WordPress?

Thanks David. We ended up removing the files and directory for Gravity Forms that were still within wp-content and then we were able to re-install. It appears that it was trying to overwrite files and could not. Anyway, we have the forms working now. One other question I have: We are using Google servers (GMail) as our email host. If we specify our email address for the admin email, should we receive the forms when a user completes them online? Yesterday, I was informed that the forms were not being received. Thanks again!
-Jason

Thanks David. I have installed the WP SMTP plugin and activated it. However, I was trying to find out what port number to add and found that the host server we are using, aspmx.l.google.com, is for applications not supporting SSL. Would we need to consider using a different host server with Google? I know the advantage, of course, is that it will be more secure. However, I am not sure which host server(s) we should use then. Thanks for any advice!

Thanks again. We will leave our host server as it is and will see if we start receiving the forms again. I have also changed the admin_email to the address we want it to go to. Not sure if that makes much difference, but thanks for your help!