I read the OP to mean that the problem was not the drivers but the physical connection. An LJ4 only has a parallel port, which most modern PCs lack.
Is wireless networking the only possibility (there are solutions but they are expensive)? If wired networking was acceptable there are cheaper solutions. Basically you want an ethernet adapter for the LJ4, either an external one or one of the HP internal ones (they were quite expensive).
Or, if you want to risk a small amount of money, go for this one on eBay
. I've no idea whether it would work with your LJ4, but can't see any reason why it wouldn't.Edit
: Here's one from the UK
if you don't want to risk the Hong Kong ones.