Sendgrid has recently done which has been leaving wordpress sites forms broken. Problem is in version 1.11.0 they finished the need for putting your logins in the plugin. Its understandable its a security risk to save such data in the database but it has left allot of sites not able to send emails.
You can see more details on changes done in version 1.11.0 by visiting the wordpress sendgrid plugin page.
To fix this problem you need to go into your sendgrid account and generate an api. This api can be used in multiple sites. Now you need to add this api into your send grid plugin settings page in wordpress admin. Once you have done this you should test to make sure sendgrid has started working again.