Please login to your control panel (at http://yourdomain/cpanel) and make sure
1) Your email account is not over quota. You can check this by clicking on Email Accounts in your control panel and it will show you how much disk space is being used by your email account.
And if your mailbox is full, you need to either delete old emails, clear your spam box from the spam assassin page (again from your control panel) or increase the quota of your email account.
You can also login to your webmail at http://yourdomain.com/webmail (username is your full email address) and go into Squirrelmail, click on Folders, subscribe to all folders, refresh the folder list, and then check all folders and see where all the disk space is being used. This is your mailbox that you need to manage.
2) Your entire hosting account disk quota can be full as well. In this case, use the Disk Usage Viewer in the control panel to find where space is being wasted and make some room, or if your disk usage needs are growing, you can upgrade your account to the next hosting plan.
Note: 99% of the time, the above two are the reason for not receiving new emails.