Yes...and no...
You mentioned that you had it rotated all the way...counterclockwise...
What can happen if the rotor is not quite on the peg inside the cap you can get a weak spark...that is why I suggested rotating the dizzy slightly and checking it each time you move it...say 1* or one singe notch...and when you did that you did get it to run...somewhat...
Now, you also mentioned that the dizzy was recently replaced...OK...so, what you may want to try is to remove the cap, note where the rotor is pointed, then remove the distributor...then you need to roll the distributor clockwise about 30* (indicating degrees) CLOCKWISE and then reseat it...if you watch the rotor or top of the dizzy, it should rotate counterclockwise about 10*...that's OK if you started out by rotating it at least 30* clockwise...
What this will do is give you a bit more swing and may actually line things up properly...or, it could throw it out some...so, again, trial and error...
I had to do this with my dizzy a couple of times till I got it right...but it will give you the blue spark if that's where the problem is...hopefully~