If you are saying that the leak appears from the horizontal seam of gray and white, I would suspect that the leak is from the roof or siding above that joint or possibly from the window. That horizontal siding part is like a custom Z-bar, where the back lip of this piece should be a couple of inches tall behind the gray siding.
This siding is pretty easy to work with. You may be able to check it after a rain by removing a lot of the screws and just lifting the siding off a little bit. You should be able to see that the leak is coming from higher than this horizontal trim piece.
The very top of the picture shows just a little bit of the top of the siding. It looks like a gutter or something has been removed from this area. The leak could be coming from this area. As the rain comes off of the roof, it could be working it's way into the top of the siding. It could be a leak at the drip rail at the top of that wall or edge of the roof in that area.
While this type of siding is old school. it is still pretty efficient and easy to work with, unless there are dents at the vertical seams where the gray siding pieces come together. It can still be taken apart and put back together, but the dents will make it more difficult. This siding can be ordered, but it is very expensive because of shipping. I am guess $100 per 4x8 sheet. The horizontal trim piece should not need replacing, but some sort of replacement is possible using the same siding material. All-Rite Aluminum Products sells this type of siding and makes custom trim pieces. Your siding pattern looks like - 4" Mesa 3 w/ reverse and this type of siding usually has the Pittsburg Edge. Here is a link.
http://www.all-rite.com/aluminum-siding-p-53.html
The cheapest repair would be to repair the siding that you have. After the repair, the home should be painted to look right. Again, I suspect the top of the siding or the edge of the roof, which shouldn't require siding or a lot in material costs for a spot repair.
Pictures showing the roof edge, the top of the siding, all seams of siding and trim in the area, and the window might help us get a better picture as to where the water is coming from.
JMO
JD