I didn't get new codes from anyone so I hit up tequipment in their online chat. They told me the "old code" I already had was supposed to still be valid, despite their system telling me it was no longer valid. The support person I talked to discussed it with his manager and verified that the code should have been working. I tried uppercase, lowercase, mixed case.. nothing worked.
What they did instead was to call me and put the order in over the phone. Then they manually applied the same percentage of discount to each item as if I'd used the code.
I ordered a JBC Extractor-Inserter Cartridge Stand and a handful of new tips and saved about $30 on the order!
If you're having trouble using the "old code" on tequipment.net it would probably be worth the trouble to contact them via chat or phone.