Demosthine: When you see people talking about hens 'only laying for 2 years', what they are really talking about is the typical drop off in production that happens after the first two years of a hen's life. This drop off in production is most severe with the high production, commercial breeds, and the high production hybrids. Also, somewhere between 18 and 24 months, chickens go through a molt, and stop laying for a month or so. If you have a commercial operation, it isn't worthwhile to feed a hen that isn't producing eggs, or who is "only" laying 2 or 3 eggs a week rather than 5 or 6 eggs a week. Many people have observed that chickens that lay fewer eggs are often more consistent producers, over their lifetime.
As a side note, when I've integrated new birds into the flock, or taken birds out of the flock, the stress of the social upheaval tends to reduce the number of eggs for awhile, and I've had fairly 'easy' flock integrations.
As far as getting a broody to take chicks goes, a week is too old. Ideally, you want chicks no more than two or three days old. And honestly, if you're willing to use the cockerels for meat, you'd be just as well off putting fertile eggs under her. Of course, this assumes that you get a broody hen to start with. Some breeds are more likely to go broody than others, but there are plenty of stories of hens from breeds that typically go broody as soon as they see an egg that never go broody. And on the other side of it, you get birds like my Emma, who is a Cali White, which people will tell you never, ever go broody, and she took off on her own and hatched 3 chicks. Of course, she may never do it again, so who knows.