You have received some excellent advise so far. The basic problem should have been realized and addressed before the home was built. Now it is too late, but this comment is meant for others that will read this post in the future..
A few things to add would be that the black perforated or solid pipe that comes in rolls has ridges in it. These ridges work to slow the movement of water and create resistance to flow. I would always prefer to see the white PVC smooth pipe used for these drainage projects for this reason. Also landscape fabric should be used in all instances to minimize any infiltration of silt. Follow carefully all the information in the French drain thread. If you increase the size of a pipe by double.... 4" to 8"...... you will increase the capacity by 4 times. For this reason, when you want to move a lot of water in a hurry, you should install extra pipes. There is no rule that restricts the number of pipes that may be laid alongside of each other, however people in their conservative financial thinking, feel that one is usually sufficient. In some applications, it might call for the use of more than 2, 3, or even 4. The time it takes to install 1 pipe vs. 4 is a small factor. Once the trench is dug, the rest is a piece of cake. If I were involved in the resolution of this problem, I wouldn't use a trencher, but a backhoe to dig the trench. Lay in landscape fabric, put down a thin bottom layer of 3/4" stone and set the down hill slope at 1/8" per foot for long runs and 1/4" slope for shorter runs assuming that you have the proper elevation to get this degree of slope. Then backfill with 3/4" stone to about 2" - 3" from the top surface. Cover the top stone with landscape fabric again, so there is no infiltration of silt in the entire trench, and then put down loam for the last 2" - 3" of soil. This trench would be at least 2' wide and 2' or more deep. The water will flow through the stone and the pipe, so this should accommodate most torrential rains. Without knowing the area that is collecting the rain water and running down toward the house, I have no way to determine how many 4" plastic pipes that you will need to accomplish this. The more the better. Remember, that you only want to do this project once and a length of plastic pipe isn't that expensive in relationship to the cost of the project or the damage that can occur if your home is flooded. This project is going to be expensive, but just consider the additional expense if you have to do it over. Do it correctly the first time and you will never regret it. One final thought.... you can also put a French drain part way up on the hill to pick up some of the water as it comes down. Also consider setting up a terrace effect so the water is slowed as it come down. If you set up the terraces properly, each terrace will act as a water collector holding some of what comes down before it rolls over the edge onto the next terrace. Then you could put in a few French drains, one on each terrace and know that with a few terraces and French drains on each one, that very little watter will reach the house barring a massive hurricane downpour. Planning is the most important step and I wouldn't rush into this project until you have a complete plan of attack. If it is a financial burden to do everything at once, then the terrace method will be the least expensive way, putting in the French drains starting at the bottom and working up the terraces as you determine how many more you will need based on experiences with future rain fall.
