While I've never had serious problems shaving such as you describe, I did find it a humungous bore and wholely unsatisfying until someone on Hacker News linked to this guy's videos: http://www.youtube.com/watch?v=-qSIP6uQ3EI

What made the real difference for me was going from multiblade razor with can of shaving foam, to multiblade razor with shaving oil, to multiblade razor with shaving soap and a proper brush, and finally that but with a neatening up afterwards using a single blade disposable. That final solution gives me a close shave and leaves my skin feeling lovely. I actually make the time to have a proper shave every day and really look forward to it!!!

YMMV, but like all hygiene stuff experimenting with new techniques is pretty useful..