I had a long post all typed up talking about null modem cables and such but got called away before it was done and others answered far more succinctly.
https://en.wikipedia.org/wiki/Null_modem
I'm glad you were able to figure out the issue.
There are other ways to connect to the 5/04 if the serial port is generally occupied, but they all require more hardware that's generally expensive. If you're going to be doing online support of a bunch of 5/04s with serial HMIs, it would make sense to connect via DH+ using either the round mini-DIN or the 3-pole Phoenix connector. The first one I saw used a PCMCIA card, but those (and laptops that can use them) are long gone. Another method I saw, that was very effective and reliable, involved the use of a spare ControlLogix chassis with a -DHRIO and an -ENBT module in it. RSLinx would pass through the backplane to get to the machine. This is doable if you happen to have the hardware laying around but would be really expensive to set up from scratch (like about $9k list price). You can go with the -U2DHP module from AB, but...they're expensive and delicate. We had a couple fail just from normal use. We also tried the
Prosoft AN-X2-AB-DHRIO gateway module with great success. They're also expensive, but they're very reliable and robust. Way more than AB's -U2DHP.
A more recent product is from Automation Networks:
https://*************************/o...lc5s-and-slc-504s-to-latest-ethernet-productsI've never used that one but it's definitely worth a try and priced at about half what we paid for the Prosoft version 3 years ago.
If you're only doing occasional work with a 5/04 and don't need to be online at the same time as a serial HMI, I would just stick with the serial cable. It's cheap, simple, and reliable. If you have a lot of 5/04s and want the HMIs to stay connected while you're online...you'll need a DH+ gateway. I would choose the AB -U2DHP last of all the options based on my previous experience with them being expensive, delicate, and not repairable.