It is my understanding that the GPL and Artistic licences apply to copying and distributing the "program". I am free to modify perl (or any other module or such licenced software) and 'use' it as I wish (whether I'm an individual or a company). If that means I create a web application based on those modified programs and run it on my server (perhaps charging a fee for usage), I am not required to release source --- because I am not "distributing" the product, merely providing a service (or, as chromatic says: I would only be providing output from a GPL'd program). Once I decide to sell, or give away, or otherwise *distribute* the application itself, then I am bound by the terms of the GPL or Artistic licence (which are different in what they actually allow me to do).

If you coded programs for "the company", the company (probably) owns those programs. They do not own any of the original open source code that your products were based on (or that your products used) and they cannot restrict your future use of such code (probably stating the obvious here). But, they do own your new code, and any modifications you made to the original code while in their employment. (Note: this interpretation is based on assuming relatively standard employment agreements you likely signed when you were hired). So, yes, they can restrict you from using code you wrote for them (which isn't really yours) to make new products.

Should you decide to "independently" recreate their modified software you may still have legal problems --- convincing a court that you recreated it independently of your work for the company may prove difficult at best (hard to claim 'clean room' status since you were intimately involved with their project).