Did ya put the SD card in 'fore pressing anything at Brawl's "press start" menu? For some reason ya need t' put it in at said screen. Can't insert the SD card before booting up Brawl/during the opening cutscene/after you press start.
You've usin' the proper region version of Project: M, yeah? 'Cause NTSC Project: M won't work on a non-NTSC Wii. Same applies t' the other region versions.
Your SD Card is 2 GB or less, yeah?
Also, try using the installer. I had the same problem and that fixed it. For whatever odd reason I couldn't just throw the P:M files in the folder and get 'em to work. It'd either freeze or simply load nothin'. Soon as the installer put the files on my SD, it worked fine.
... But the Klaw is still better. Bowser can JC the Bowser Bomb t' jump quicker and outright higher, so it ain't like he has no mobility options in P:M.