Should I allow my partner to walk away from our business but retain his ownership of our trademark?
Here's the skinny: Generally, what a business partner creates for the benefit of the business while a partner of the business belongs to the business, not the partner. Exceptions can arise if the website (or other intellectual property) was the partner's preexisting intellectual property--but that doesn't sound like your situation here.
As to the "buyout price," the intellectual property and brand name could well be a significant part of the company's value, separate and apart from its performance.
And it's not unheard of for partners to wait to get paid when the company is sold (especially if there's little value to the company now--so he's waiting to strike it big when that time comes).
But as the continuing owner of the company, do you really want that albatross around your neck? What if you don't sell for another 20 years? Is his startup input for the first three years really a fair trade?
This is not the kind of negotiation you'll want to handle on your own--find an attorney in your area who's familiar with these kinds of buyout issues so that you can get the professional guidance you'll want to make sure you're protected fairly.