I can make up a new key and compare it against all the existing keys, That's millions of chances per key I make up ? I do this for one month, Surely I must find loads of matches? What am I missing here? Thanks
Well, math and the laws of physics are against you...
This image is never going to get old.

And all these keys are stored somewhere (where? on the blockchain?) What's to stop me just searching through the whole blockchain for a match?
The keys are not stored in the chain. The blockchain is a ledger of the transactions.
I recommend you start reading
https://en.bitcoin.it/wiki/Main_Page before you waste your life searching for a match.
That means that your probability of finding it is inbetween 16-32! (the ! is a probability thing) and those numbers are probably in the trillions if I had to guess. If you feel lucky enough you can find one in the trillions by all means go for it but you would spend forever.
One trillion is just a puny 2^40, think more of 2^96 when you try to match private keys.