Try oil lemon oil or teak oil or mineral oil. I hope you haven't tried anything else. Oil works but it is easier if it is not altered by other chemicals. Cooking oil is good for removing label and price sticker glue from glass or ceramics too. In fact almost any kind of tape glue is removable with oil--something to keep in mind for the next time you want to remove tape glue. Since I found this hint it's the only thing I use.

Westond,I'm not trying to be rude when i suggest you reconsider doing this yourself. The point I want to make is that you must have some degree of judgement on what you are looking at while performing a task such as this (largly due to the enormous collective weight of all that brick). At minium one should have have played with legos and dominoes rather than vidio games as a kid to know that the intire fireplace will fall on you if you remove a few of the wrong bricks before removing others from above. The pics are interesting and you have a nice place but I don't need pictures to tell you the fireplace is not holding your house up. Look at your own pics (better still,the house) and it's obiovus the brick in last pic is only one brick deep. I realize the little "soldiers" at top in last pic might appear to be holding the ceiling/floor up but they are there to fill a gap and do not support a thing. There are things that should never be attempted without a basic understanding because you can't get it off the net despite what some believe. Think of it like this,with mortor falling out as you say yours has,the brick would shift and alow house to fall if house was supported by brick in fireplace. Removing the fireplace is a grunt job,hire some experienced grunts and spend your time doing what you do to earn a living or just go fishing. Fixing the hole after brick are gone require's even more construction skill so be prepared to hire a finish carpenter.

From the desperate folks do desperate deeds department: I wouldn't want to warrant that defeating those fasteners will allow you to lift the cabinet bottom, but if you think it will and want to try it, you might try cutting the panel around them with a slightly larger hole saw. Use a high quality one with a drill bit you can remove from the arbor. With the bit still in, cut a hole in a piece of 1x scrap stock. Fasten the scrap stock to the cabinet bottom over the area to be cut, using drywall screws or something similar (you'll have to patch the holes later). Remove the drill bit from the hole saw and have at it. The scrap will stabilize the hole saw so it won't run amok without its drill bit. How to re-secure the cabinet bottom later will be left as an exercise for the reader. :)

Pretty easy job. If you are replacing the carpet, even less to worry about. Consider what is behind the fireplace wall. When you remove the firebox, you may be able to free up some space on the other side of that wall as well. Consider how it is vented. If it is a direct vent fireplace, then some patching will need to be done outside the house or the vent pipe will need to be blocked off somehow. Gas line will need to be capped, so technically, a plumber would be involved, although it's something you can do yourself. Really, depending on how that fireplace is installed, you can probably do it yourself if you are handy with drywall.