If you have a very efficient modern gas furnace that has a high moisture exhaust it is possible that you could direct vent it with a PVC pipe right out the sidewall of your house. Then you could just forget about your chimney and cap it and seal all inlets (unless you have other fuel burning appliances that are using it). You need to find out the model number and check with the dealer or installer to be 100% certain that this is possible with your exact unit. Then you can have them come in and do the new pvc chimney. If you can do this with your unit then you can get away with just spending a few 100 $. Otherwise, if you can't then the stainless liner and new cap are probably the only way to go and the price seems to be in the ballpark. If you decide to get more quotes from chimney sweeps then be careful because while there are many reputable chimney sweeps there are also some corner cutting fly-by-nighters that might give you an inferior product.
I would get a second opinion but I would guess that they will confirm the sorry state of your flue. This situation has the potential to be extremely dangerous and it is possible that you shouldn't be using the boiler until it is fixed. Do you have a carbon monoxide detector (available at hardware stores and home centers) in your house, especially in spaces abutting the chimney? I would.
I wouldn't "shoot the messenger" by getting frustrated with the tradespeople assuming you have piles of money laying around. If you want heat and hotwater, and you want to live in a safe home then you need to do these things (repair and maintenance). If your chimney needs repair then they are doing you a service by pointing this out to you.