Let readers upload large files

I have a Wordpress photography site and need to let users upload files larger than 10MB. I already increased upload_max_filesize in my php.ini to 30M.
I created a form using Fast Secure Contact Form and allowed files large up to 20M.
However, any time I try to upload a file bigger than 10MB, the form serves a blank page instead of the success notification.
What else can I do?

Try setting the maximum execution time higher.

Check the errors from the $_FILES

Thank you, I already set the maximum execution time to 480, do you think it is enough?
What do you mean with $_FILES?

http://www.php.net/manual/en/features.file-upload.errors.php

When you changed the maximum upload size, did you restart the server afterwards?

My site is hosted on bluehost, I don’t know how to restart the server. Anyways, I already increased the upload limit in the past and it didn’t require a restart.
Thank you for the manual page but, where should I find the file array with the error codes?

On the form for the uploading, what is the field called for the upload?

Is the new value for the memory limit showing ok in phpinfo() ?

The form uses an input field of type file. You can see it here: http://www.fotocomefare.com/rubrica-giorgio-trucco/

If I execute http://www.fotocomefare.com/info.php, all the settings are as I set them.