If it was a hardware issue digital ocean would be aware of it. You are using a VPS cloud so you are not an isolated user with dedicated hardware.
You are having the same sort of problems you were having with your shared hosting.
Code:
root@paragon-DS-7:/var/log/mysql# zcat error.log.4.gz
root@paragon-DS-7:$ cat /var/log/apache2/error.log
Check your MySQL and Apache2 logs for any errors or information (if you haven't already).
check your PHP code.
Code:
$ php file.php > file_name_warnings.txt