Did I drop too much yeast to carbonate my bottles?

I bottled an extract batch of AHBS 4 Hearted Ale 6 weeks ago and still have VERY little carbonation. The bottles have been stored in the warmest part of my house which is in the 72-74* range. I did use priming sugar but thought I would clear up my brew a bit and cold crashed it for 36 hours prior to bottling as I was under the assumtion that I would still have enough yeast to carbonate. I also have very little yeast settled on the bottom of the bottles and the beer is very clear. Did I drop too much yeast prior to bottling? Can I use a sanitized eye dropper and some yeast from a starter and re-introduce some into the bottles? If so would I be better off using yeast from the bottom of the starter after refrigeration or directly from an active starter? I am sure I could also wait it out longer but I figured 6 weeks is a pretty good indication I did something wrong.

If you see some sediment at the bottom of the bottle, there should be enough to carb them. It may take a little longer than you are expecting. I had this happen once, so i rolled the bottles across the floor to re-suspend the remaining yeast, and let them sit for a few more weeks. Assuming the proper amount of priming sugar, and that they have produced even some carbonation, they should eventually carb up to your desired level.

It is impossible for a homebrewer to remove enough yeast to prevent carbonation. It takes sub-micron filters to remove all of the yeast.

I agree with arkador, resuspend the yeast and give them a couple more weeks. I've had beers take 6-8 weeks to carb up.