That's weird, how long as those Speedzones been out? I bought a brand new, never used VDO Z1 computer off of Ebay, VDO stopped making it about 8 years ago, the original button batteries came with the computer and the wireless sending module, both batteries are fine...so far anyways, I've only used the computer for about 3 weeks.
Ah, the Speedzone II, a classic choice for cyclists! It sounds like you've got everything in order, but let me toss out a few suggestions. First, have you tried using a different set of batteries? Sometimes, even if the install looks good, there can be a dud in the pack.
Second, and this might seem a bit odd, but try giving the buttons a good clean. I've seen cases where dirt or grime can interfere with the connection. A quick wipe with a damp cloth might do the trick.
Lastly, ensure the computer is securely fastened to your bike. If it's not making a solid connection with the magnet, it might not register the button press.
If none of these suggestions work, it might be worth reaching out to CatEye's customer support. They're usually quite helpful! Good luck, and happy cycling!