I've done some research and found that yellowing/browning on the base can happen for several reasons.
My guess is it is root rot because it is winter now and we have probably over watered inside.
To me it looks like it is dying and may not recover, I read one post that said cutting off the top and replanting it may save it. Is that true? Any advice on how to get it back to health would be greatly appreciated.
It's hard to say why it's rotten, but from the pictures the stem down at soil level looks almost black. I suspect that this is a dead plant. Push gently on it at the very base with a pencil or something (the blunt end). If it is soft, you should probably take it out of it's pot to get a better view of what's going on.
If it truly is rotten, it may be possible to cut the green part off and root that. If you cut the top off use a sharp knife and wipe the knife with alcohol if possible to avoid passing pathogens. When cutting it off make sure there is no sign of brown rot on the part you're keeping.
If it makes you feel any better, I've been raising cactus for years and have killed more than my share.
I agree with what others have written. Before even seeing the pictures I thought it was perhaps the result of overwatering. Often times our instinct is to add water when a plant turns yellow and then when it becomes even more yellow what do we do? Add more water! I would try to repot and place in warm sunny spot, it may turn around. Good luck!
It is always worrying more when discoloration starts at the base. Often you spot the issue as it starts and taking a cutting from the top part can save the day.
My advice is to check how sturdy the plant is before adding water. Any signs the plant is too easy to bend side-to-side may warrant an inspection of the roots. Another sign is that the plant does not respond to watering. Check the roots even after your first time. The right approach is critical with the more spiny species: As a novice many years ago, few looked fine to me. After few months of not growing, I realized I was watering a hollow shell of intertwined spines.
