Panic. Run around like a chook with its head cut off.
Unless you have a support agreement, then you are sweet. You’ll only have a support agreement if you’ve got a plan to migrate away from Server 2003. So while it’s not great that you’re still on Server 2003, you’re at least doing something to get rid of it.
There are going to be some workplaces where Server 2003 is going to be around for some time. This is because management has a “if it works, don’t mess with it” philosophy.
A friend’s dad is an architect. He’s semi-retired and used the same PC for the last 10 years running Windows XP. This PC runs a version of AutoCAD from the 1990’s that the dad uses for his architecture practice. This version of AutoCAD doesn't work on Vista or later.
When Windows XP’s end of support expired, the friend explained the issues. The architect didn’t want to migrate to a newer OS because it would mean going from the software he was quite happy with to a radically newer version that not only did he not want to learn, but would require an annual subscription. The friend told his dad that the hardware he was using was going to fail at some point, but the architect said he’d cross that bridge when he came to it as he was semi-retired and was still working because he enjoyed it rather than to pay the bills.
So the solution was to disconnect the computer with AutoCAD from the Internet, to get the architect a basic laptop running Windows 8.1 that he would use for every other task other than designing buildings, and to have him transfer files across using USB when it was necessary. The architect was fine with that because it would still cost less than acquiring and licensing the new version of AutoCAD.
This sort of kludge might work with Server 2003 now that support has expired.
If you are still running Windows Server 2003, it’s likely time to do your best to isolate those workloads from the Internet. Isolating those workloads won’t get you around compliance issues with running Windows Server 2003, but it’s better than keeping them connected, even indirectly, to the internet.
What you really need to do is migrate. If management can’t be convinced at this point to do that, you’re probably stuck between a rock and a hard place.