Your symptom is definitely pointing to a PROM connection problem of some kind. Even with no hard disk installed you should get a solid green light on the front and a "TiVo Sunrise" on the TV.
It's hard to tell from your photo, but it's possible you have some pins bridged. Inspect them closely with a magnifying glass.
Additionally, if the solder you're using has rosin flux, make extra sure it's completely cleaned off with high purity alcohol or ideally a flux remover of some kind. I've seen problems crop up when flux creeps up the pins in the socket and prevent a good connection to the chip.
Moving a CableCARD, even to a different slot the same TiVo, will break its pairing. The only time you can do this is if the cable company doesn't even bother pairing the cards. I only know of one company that has ever done this, and that was my old provider in Iowa, Mediacom.