Chimney cap, liner, oil burner, etc....

Houe built around 1900. Coal conversion to oil at some point. Original burner.
The cap blew off my chimney the other day (oil burner only - no fireplace).
So... I called around and got someone to come and do a clean and a replacement cap.
Turns out the tile lining in the chimney is cracked - somewhat badly. They first thought it was only where the exhaust for the hot water heater was put into the chimney, but upon further inspection, it was in a variety of places (some tiles had broken and fallen down).
First idea was to patch it when it was only a few tiles, but when it was all over, they suggested a replacement liner. Which of coruse involves removing the existing liner since the diameter of the flue would be too small to take the exhaust from both appliances.
So the situation has gone from a few hundred buck for the cap and cleaning to a considerable sum for all the rest of this work.
Here's another wrinkle... the inside of the chimney cap that blew off seemed to be scortched to the point where the guy who came said he thought the burner was running too hot. This leads me to thinking about replacing the 70 something year old oil burner and get a new efficient model. If this is the case, I MAY be able to get away without tearing out the existing liner and just putting a new liner in (or so I am told by the chimney guy - who I would tend to beleive in that case since it would be less money for him to do that job as opposed to the "pull out the old liner first" job).
So do I....
1. Fix the existing problem, keeping the old burner, and just do the liner work? If so, any idea as to how much that should run? Seems to be about 35 feet of liner needed, tear out old, install a new one, etc. I understand there is lightweight and heavier duty liner.
OR....
2. Upgrade the oil system to something new and just snake down a new liner inside the existing one? Same questions... how much, etc.
Hot water radiators, 3BR's on 2nd floor, LR/DR/Kitchen on 1st. Attic and Basement not heated. Northern NJ (Bergen County).
Thanks... forgive any incorrect jargon or terms... I am very clueless about these things...
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A few cracks don`t make it dangerous in itself it depends on chimney condition. Remove a liner, how, its in there solid. Depending on flue size a ballon is inflated and concrete poured around it for a liner.
But I would get a few more opinions, best might be someone you pay who is not biased by getting a job.
Scorched top, oil burner=soot. A 65 yr old oil burner is not going to be nearly as efficient as the best you can get today, you might honestly cut your bills 30-50% +. Then if you change if Ng is available, that is an option which may or may not be cheaper now per Btu as Ng for most has gone up more than oil and may continue the disparity for some many many years . Find out how efficient your unit is and run your numbers, only you can do this.
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