|Keep It Simple, Stupid|
I sympathize, having worked my day job mainly on a Solaris/Oracle system for many years. First some comments:
With respect , this isn't really your problem.
From what you describe:
This reeks or management/business decision issues, which the company (not you specifically) should address. It's clear to anyone reading this that you have good intentions, the company should support and enable you to fix their problems, either by giving you the access you need, or at least having someone properly support these production systems.
Each version of Oracle ships with it's own version of perl, hidden in the train wreck of the application install that is Oracle, are you confusing the system perl with this, or are you getting confused by the number of different builds/DBD::Oracle builds?
My first recommendation would be to install your own modern perl somewhere on the system, and once you're happy you have all the options right. Our stack was somewhat similar, except that I setup a modern build environment, as what ships with Solaris is so old.
"Is there anyway I can figure out based on the previous Perl install?"
You likely know that perl -V will provide compile time information.
My suggestion is that you take a step back and start from scratch. Read INSTALL and README.solaris (patch inbound, some of those links are long dead), as well as the DBD::Oracle documentation and hints.
If you still have troubles post a concrete example of what you tried, how it failed and details of your setup (compiler etc).