You should have access to Apache error logs. If you can’t find them, ask namecheap where they are located.
Uploading osTicket Awesome from scratch won’t hurt. Just backup your /include/ost-config.php file before you do anything.
Also, you should download osTicket v1.14.1, upload the upload/ directory, rename it to osticket-vanilla/, and then copy your ost-config.php file to osticket-vanilla/include/.
Now you can go to yourdomain.com/osticket-vanilla/scp and try posting a new ticket. Does it work?