Is there a transaction book in which to look for the mined bitcoins?
No.
The Bitcoin blockchain is a transaction journal, but it does not link mining rewards to people’s names.
In March 2008, I joined a bitcoin mining program
I recall the Bitcoin “whitepaper” was written only in late 2008 and published early 2009. So it was impossible to mine Bitcoin in March 2008 – Bitcoin didn’t exist. The first block mined, the so-called Genesis block, was mined on Jan. 3, 2009.