This is confusing to me. Maybe not your wealth, but your ability to mine new Bitcoins is determined primarily by your computing power.
Your wealth in bitcoins, just like your wealth in USD or EUR or any other currency, is determined primarily by what you can produce and sell to others, including your labor, with a bit of the luck of life thrown in, since life isn't fair.
Working on mining new bitcoins is really more like helping make sure transactions go through. So, much like Visa/Mastercard/Amex/other banks manage to get some wealth by processing other people's transactions in traditional currencies (and they've spent resources at having that happen), people can get some wealth by processing other people's transactions in bitcoin. But, you need to spend resources to do so (such as computing power), so you still are really selling your labor and products to others to get something. It's just that bitcoin breaks the monopoly of traditional payment processors and lets anybody process transactions and get compensated for it. Hopefully, the long-term result is that this will end up with the cost of transactions being close to what a transaction actually costs to process, instead of including a profit margin for banks since there isn't as much competition for payment processing now as would be ideal.
And what's this about new Bitcoins being divided up among the nodes? I haven't gotten any fractional new blocks given to me. New blocks go completely to whoever found them, right?
Yes, new blocks go completely to whomever found them, although if the block is found as part of a pooled effort, then a portion would be yours. What it's trying to say is that in the probabilistic long run, blocks are given out in proportion to the hashes/sec supplied, so that an entity with 2000 khash/sec will get twice as many blocks as an entity with 1000 khash/sec. So, in that sense, the "new bitcoin supply" is divided amongst all miners in the right proportions. Now that 1000 khash/sec will take 609 days on average (and likely more as the difficulty keeps on going up), it may seem strange to say that if you're 0.00001% of the hashing network that you'll get 0.00001% of the blocks and thus 0.00001% of the total bitcoins yet to be distributed, since it feels more like a lottery at that point, but if you were to be that percentage of the hashing on the network until the end of time (and bitcoin lasts that long), then that's what you should get. On average, of course.
But mining should really be thought of as "running a payment processing system for bitcoin like a credit card processor, that I might get paid for", not like "running bitcoin". Running bitcoin is much more like "I have a bank account." or "I have a wallet."