Ok, I screwed up. I have minus signs for the idle periods, but it doesn't work that way. The raw sender assumes the periods alternate between carrier and no-carrier, and all the values are positive. So we need to remove the minus signs. Actually, I've fixed the code in post #23, so just get it again from there, and run it again.
I found a raw sender example that works. It's the IRsendRawDemo example in IRremote v2.8.0. I don't know if you want to bother with the old version, but that's all I use.
That example sends the code twice - once from ram, and again directly from flash using PROGMEN. The latter just doesn't work at all, so I'd suggest you comment it out.
We would need to get the PROGMEM method working though if you're going to send raw. There isn't enough ram to hold very many keys. But I'm hoping we can find the protocol for the cable remote and send the codes in hex.
By the way, in the example it looks like you can change 38KHz to 40KHz for Sony.
Anyway, please post what you get in my sketch when pressing a number key on the cable remote. Maybe someone can identify the protocol.