I am not an expert, either. But I have too been using a GoDaddy VPS for quite a while. Right now I have a Linux 4GB RAM, 120GB HD VPS, and I hate to say this, it has been running great. I got this VPS in January, and it has been solid for this entire year.
Okay, back to some ideas.
1) Have you done a graceful reboot recently? If not, give it a try.
2) From SSH, issues a "TOP" command and see if anything looks strange.
3) In Moodle, go to Site Admin, Development, and clear your Moodle cache.
4) While in SSH, issue a "df" and see if you are short on disk space.
Now, on to more time-consuming issues.
1) What version of php are you running, and which database? Are they somewhat current?
2) How big is your database? Do you back it up? How big is the backup?
3) Have you considered upgrading Moodle? I am running the latest Moodle, php 7, and MariaDB.
Now, this might seem a little weird, and GoDaddy will probably not be able to help.
1) I was having some problems with my previous VPS. I was convinced that it had to be a different user excessively consuming database resource. GoDaddy didn't help me. But every month, my database server would have problems. I had it down to the day and hour. That's one major reason why I purchased a new VPS this year. Problem gone! Yep, weird way to fix a problem.