The whole thing was rebuilt using new tech; Java for the most part, cloud-ish hosting (our "own" bare metal servers and OpenShift via a Norwegian company), and this stack was never a problem. In fact, not much was a problem, because:
The old system was _riddled_ with unit tests that could easily be replicated in any language. All of the bugs and/or minor issues over the last 30 years had been documented and had unit tests covering them. This was what saved the rewrite. Our rewrite could rely a lot on TDD based on those tests, which made it possible for us to trap problems early on.
Without those tests - written by programmers who probably are long dead - the rewrite would never have succeeded, or at least not in the time frame given, and at least not on budget.
Since then, whenever our consulting company is involved in anything that has to do with existing software, we ask the client about how their test coverage is;
* None, but you will give us $1 million per hour? Nah. Doesn't matter. Find someone else.
* Lots, and you'll pay us $1,000 per hour? Tell us more.
So: create (unit) tests for _everything_. Fixed a bug? Create a test for it. Changed some behaviour? Create a test for it. Removed a feature? Create a test for it.
EDIT: Final stack looked like this:
* Self-ish-hosted servers (non-Norwegian cloud providers was not an alternative because of privacy issues).
* Java as main programming language on the backend, but many services was written in C#.
* Frontend didn't have to be fancy, so some simple JS-stuff there; think auto-complete, no fancy DOM-handling or anything like that. Application as a whole was very server-centric.
From what I've heard, they are now trying to get away from Java, and move more and more over to C#. I just hope they keep the unit tests. :)