Looking at alternative solutions - could you go wireless?
Failing that, you could consider using VDSL media converters, but if there are a lot of ports, it could get expensive quickly.
If you have Cat3 cabling - VDSL would be the only way to use that cabling.
If you have Cat5, you could look at using 100Mb/s only - but personally, I would rather change to WiFi.
I think I would get a cabling company in, get a quote and confirm what kind of cabling is installed.