We bought the house knowing there was a problem. The fireplace surround was leaning off the wall into the family room. After removing the fireplace and part of the subfloor, I have found quite a few other problems in the very small dirt crawl space.
1) The main joist running across the room needs to be raised on one end (the corner that touches the foundation has rotted).
2) Water pools in the crawl near the middle sill.
3) A barrier of some kind need to be installed preventing water getting into the ground.
4)Ground water needs to be diverted out of the crawl space.

Any ideas on how can I solve these problems?

Because the information you give isn't clear, it's hard to make any recommendations. I'm not sure what you mean by "main joist"...all joists are created equal; there is no main joist. Perhaps you meant "main girder". Whatever it is, it needs attention. If it's a girder that's rotted, it needs to be replaced. If it's a joist, it needs to be sistered full length.

I assume your crawl space has an earth floor. First of all, it needs a carefully installed vapor retarder, to keep moisture from the ground from entering the crawl space. Then, it needs to be ventilated.

If you have a real ground water problem, you probably need to grade the crawl space floor so that it slopes to one corner, and install a sump pump there.

That's about the best I can do without a clearer picture of what's going on there.

The main joist or girder, is the lowest one. What I mean by that is it spans from one side of the foundation to the other and sits on a sill in the middle. Above it, and supported by it are other "joists?" that run perpendicular. Those have the subfloor placed onto them.

Would a vapor retarder be applied to the ground, or above on the joists?

Lastly, would grading be done with pea gravel or just a slope of dirt?

Thank you for your help, it is much appreciated.

Two thoughts come to mind.
Sell or spend lots of cash.

If the beam in the cawl space has rotted and dropped. You will need to jack the floor up and replace it with the same size beam. If you want to cut out a section like Richard said. You will need to install a new footing and column to hold up the spliced section. This is not a do it yourself type of project. Its best left for the professional as doing this wrong can lead to many more structural issues pretty fast.

Be sure to choose a contractor that understands jacking and strutural framing on homes. Lots to claim they understand this but most do not. So be sure that you got the right person. You will know when you get them as you will find the cost is higher then most of the rest. But done properly you will end up saving more overall as there will be no mistakes to fix later.

Ventilation, vapor barrier and water issues I agree with Richard on that as well.

We are starting a project very similar to yours on Monday, but more severe. The crawlspace is approx. 12" deep so all work will be done from removing the flooring above and doing it that way. Total estimate for the job $58,000. I will never bid one of these jobs firmly - that would professional suicide. I would expect your project to run about $15,000 - $20,000 depending on a number of factors. Probably not what you wanted to hear.

The vapor retarder goes on the ground, and should be at least 6 mil polyethylene sheet, with all joints lapped 6 inches and fully taped, and turned up all walls and other penetrations such as columns, piers or pipes, and fully taped to them also.

There should also be another vapor retarder up against the subfloor, which is usually part of the insulation.

Derek -

If you are in a heating limate (MI), the vapor barrier on the first floor insulation should be on the warm side of the floor insulation.

If there is none, then you can do as you choose with that vapor barrier.

Not so. If there is no vapor retarder up against the subfloor, and one were to install a vapor retarder below the insulation (on the bottoms of the joists), one would be quickly dealing with wet insulation, and possible mold and, after a time, structural decay.

Placement of a vapor retarder is critical, and a vapor retarder in the wrong place can be disastrous.

Whether there is a vapor retarder against the subfloor or not, there must be a vapor retarder on the crawl space floor.

There should be some cross ventilation of the crawl space. Installing plastic on the floor of the space is not a substitute for correcting any grading issues outside of the foundation walls. Since there appear to be no footer drains, gravel would not be a good choice as it will promote drainage into the area, instead of preventing it.