Hi,

13/10/2015 18:00 - Alex Zimmerman wrote:
> I just inherited the job of updating our production IT HelpDesk server 
> from a IT tech that is no longer here.  Due to the nature of our setup 
> in cannot be down for very long, which is why it was left to get so 
> far behind.

Typical (bad) scenario. Solution? Managed OTRS. Sorry that I am commercial 
on the mailing list, but actually this is an issue. And can be solved with 
a managed OTRS.

> The server is currently running on OTRS 3.1.3 on a Ubuntu Linux 
> 12.04 LTS server.
> (...)
> It sounds like I have to update from to every subversion e.g.
> 3.1.3 -> 3.1.4 -> 3.2.1 -> 3.2.2.... etc..

Nope. What you describe is "Patch Release" Updates...

If you read the documentation carefully you'll find:
,---
| Within a single minor version you can skip patch level releases if
| you want to upgrade. For instance you can upgrade directly from
| OTRS 4 patchlevel 2 to version 4 patchlevel 6.
`---

So you need to go to:
3.2.x -> 3.3.x -> 4.0.x -> 5.0.x
(x = latest patch)

> Is is possible to just perform fresh install of the latest OTRS 
> and import and upgrade the database?

No. You have to follow the path. Good Luck. :)

-- 
Florian