As bc says, go easy. I'd say that if you have to 'step up' your effort to mechanical equipment, you're running a good chance of damaging the pipe. But, again, as he says, it won't matter anyway since the pipe is clogged. You'll have to replace it anyway.
Flex pipe is usually used where the terrain is rocky and you need to make 'turns' with the pipe. IF you end up redoing this job, look into perforated PVC. That is, of course, if your 'run' is straight.
Here's a good link for what you'd need to do. Intro to Landscape Drainage. Towards the bottom of the page, there's a link to Constructing a French Drain. Do understand the WHOLE picture before you 'just do it'. And as bc says, where the article talks about using Landscape Fabric, use Filter Fabric. It can be had at a quarry, stone & gravel yard, or the like. If you can't find it, post up, or e-mail me directly.