Hello CBatt.
I'll try to address the several different scnearios that were discussed here.
First, you've discovered the real nuisance in the fact that today's computers no longer have parallel ports to saddle to our old trusty workhorses.
You have several options.
1) You could install a
PCI Parallel Port Card - Many of my customers have preferred this method. Ofcourse, I usually do the install, but they are almost plug and play. You may just need to install a driver. This gives your computer the ability to work directly with the printer as it was intended with the exception of old DOS programs (which you aren't still using one of those TOO are you?). Once the card is installed, windows should be able to scan for hardware changes and detect the printer.
2) You can use a USB to Parallel adapter as you have tried. These usually work, but can cause problems and again will not work with old DOS programs (you know, I'm going to stop mentioning DOS programs because they pretty much won't work properly under any circumstance without some severe tweaking). Sometimes there are issues that need to be dealt with but it really should've worked for you. First you plug in the adapter and install the driver, then you plug in the printer and have windows scan for new hardware. It should install the printer. This is probably the simplest method you could possibly use, and I would give it another shot to find out why it isn't working. There really is no reason for this to not work unless you just need a different adapter - not all adapters are created equal.
3) Next, you can install a JetDirect card like you suggested. This gives your printer networking capabilities. Great. Except you don't have an ethernet connection where you need it. Yes, you can plug your printer directly into your computer's LAN port with an ethernet cable. But, its complicated. You'll need to do a few things to make this work. 1. You'll have to use a
Crossover Ethernet Cable to connect your computer to your printer. 2. You'll have to configure a static IP address on your computer's LAN card, and your printer's JetDirect card. As an example, that will work, you can go into the TCP/IP properties of your "Local Area Connection" wired connection and set a static IP address of 10.0.20.1, and a subnet mask of 255.255.255.0. Leave everything else blank (gateway and dns). Then, configure a static IP address on your JetDirect card. You do that through your printer's front control panel. You'll do the same thing but use a slightly different IP address. Set your printer to 10.0.20.2 and subnet 255.255.255.0. Leave everything else blank. Configuring your network settings through the printer's control panel is a little bit confusing if you have never done it. You'll have to disable DHCP or Automatic Configuration then proceed to manually specify the settings. Once you do this, you'll have to install the new connection in windows. You go into Devices and printers and "add a new printer." You'll choose to add a "Local" printer (NOT a network printer), then you'll "Create a new port", choose TCP/IP port, and enter in the IP address/hostname of 10.0.20.2. Allow Windows to "query the printer" to find out which driver it needs and if it has drivers for that printer that should be all you need to do.
4) You could make the printer wireless and connect it into your existing network for all computers to use. To be clear it will not be possible with most off the shelf wireless routers. Instead, you'll need to purchase a
Wireless Bridge or hack the heck out of some of the more capable wireless routers. This allows you to connect a device with only "wired" capability to your wireless network. Again, you will have to set a staic IP address on your JetDirect card but this time it will have to match your existing network properties. But, seriously, this is starting to get so complicated use one of the other three methods - it's just starting to get ridiculous now.

If you really want the printer to be available to every computer on the network, use the opportunity to get some exercise and plug the printer in over by your router.
