How should I troubleshoot and unclog an outdoor drain?
One frequent cause of backups is that a root from a tree or large bush has grown into the pipe. If that's happened to you, you'll need to dig up the clogged area to sever the root and then repair the pipe, or if it's a porous drain pipe, wrap it in a landscaping fabric.

As Tester says, use a snake to see what you can find. You can also measure the distance until the snake gets stuck to get an idea of where you need to dig. Pay attention to any bends you feel the snake making on the off chance it isn't a straight run to the front.

Once you have an idea from one side, I'd fill the drain up with water on a dry day and see if you can find the outlet. Then try snaking from that outlet as well since the clog may be a long one from sediment building up over time. Again, measure the distance, and now you'll have an overall area to check.