Gigabit ethernet actually uses all 4 pairs (cf. https://en.wikipedia.org/wiki/Gigabit_Ethernet#1000BASE-T). So unless you want to drop down to a 100 Mbit link, you're going to need all wires in the cable. If you're willing to drop down to 100 Mbit, I suppose you could rewire the connectors on both ends and use the Blue/White Blue or White Brown/Brown pair for pins 1 and 6 respectively. Those pairs are not used in the 100BaseT standard (source: https://www.hardwaresecrets.com/how-gigabit-ethernet-works/):
Pin Color Function
1 White with Green +TD
2 Green -TD
3 White with Orange +RD
4 Blue Not Used
5 White with Blue Not Used
6 Orange -RD
7 White with Brown Not Used
8 Brown Not Used
Before you go down that path, though, do you know exactly where the problem is in the cable? Fancy cable testers can find the exact location of the fault. If you don't have access to one of those, you could also just try to replace the connectors on both ends. It's possible (perhaps even likely) the fault is there.
Finally; any chance the cable was installed in a conduit? If it was, it may be possible to pull an additional cable next to it, or to replace the cable by pulling a new one through the conduit.