Just happened to think of another ridiculously simple explanation for why this sometimes happens. Are you sure you've threaded the top thread through the needle correctly? Sometimes, the sewing gods, in their infinite wisdom, cause the thread to come out of the needle. Then, you lower and raise the needle countless times, but it just refuses to catch the bobbin. You look for every possible explanation, and it hits you about an hour later - the needle has become unthreaded.
Since you make reference to changing the top thread and the needle, this probably isn't the cause. However, if it happened at first, then you threaded the needle with the new thread in the wrong direction (most machines are front-to-back) it would continue the problem.
If that's not the problem, be sure you have put the bobbin in properly, so that it feeds the way it needs to. Moosie cited this, so by now you've probably checked. The direction varies from machine to machine. My Bernina has to be fed so the thread comes off clockwise. However, my Memory Craft Janome models have to be counter clockwise. Check your manual to be certain.
Also, once you place your bobbin in the assembly, there is usually a point that the thread must go through and "lock". In all 3 of my machines, you definitely feel it click into place. Again, your manual will tell you where this point is. In many machines, you'll find a red dot on the assembly. Be sure to have the thread locked in place within the bobbin assembly.
Just wracking my brain to think of anything I can for your problem...I'm sure it's something simple that we're overlooking. I'll keep thinking about this one. Let us know if any of these measures brings success. It'll drive me nuts until you do!!!