Have you tried each of the two 8GB modules by itself?
The first thought that comes into my mind when you state that when you put in both modules it won't boot, and it only sometimes boots when you put in one of the new modules by itself is that you may have one good and one bad RAM module.
Try booting with each of the new RAM modules by itself, if it boots with one but not with the other, then you should return the faulty module to your supplier and get a replacement.
If that's not your problem, I'm also a bit confused about which 13" MacBook Pro you have: the information you give is a bit contradictory, as I don't find one labelled "early 2011" that has a 2.4GHz processor.
According to Crucial, the 2.4 GHz 13" Core 2 Duo Macbook Pro MC374LL/A (presumably from before 2011 when the "early/late year" designation started being used) only supports 8 GB of RAM.
On the other hand, Crucial states that the early 2011 13 inch model does support 16GB of RAM...but its CPU speed is 2.3GHz, not the 2.4GHz you specify: 2.3 GHz Core i7 Early-2011.
If instead you're mistaken about the "early" designation, you might have the 2.4GHz Core i5 Late-2011 , which according to Crucial also supports 16GB.
In summary, it seems that if the processor on your 13" MacBook Pro is a Core i5 or Core i7, then you should be able to upgrade to 16GB, if it's the Core 2 Duo, then according to Crucial your maximum should be 8GB.