I'm now sharing a very 80s office in sunny downtown Whanganui.  Previously it housed a bank.

On our floor there are two sets of network ports.  One lot has blue cabling, is clearly relatively new, and cabled to a patch panel on another floor (sigh).

The other lot has grey cabling and a patch panel that looks like this: 

The jackpoints they connect to look like this.  Most don't have the extra phone cables coming out, thankfully.  Behind the little doors are RJ45 jacks: 

It comes with little plugs that fit into the punchdown blocks and take 2 pairs to an RJ45 plug.  These will pass 100Mbps.  I've tried punching down all four pairs of some Cat5e onto a port on the patchpanel, and plugging the cable into a gigabit switch, but I don't get anything.  This could be due to my poor cabling skills, though.

I'd love to see if the existing cabling could be persuaded to pass GigE, at least over a short distance, as the fibre install was requested to put the ONT near some of these jacks, not near the patch panel or any of the newer cabling.  We don't want to change the install request as it's taken long enough as it is already, and the design has been signed off by the building owner.

What is this style of patch panel called?  Can I get more plugs that go into it, that take all 4 pairs to an RJ45 plug?  Is there any hope of this cabling passing GigE or should I just give up now?