For a finance person, you'll need to work with him on calculating the cost of downtime.
At some point he'll say "OK, so if that server fails and has no warranty, I'll need to spend $x to buy a part, and we'll be offline for one day", you say "but they don't make them any more, so what you will have is a surprise hunt through eBay which may or may not be fruitful. If the latter occurs, you're in for a surprise new server whether you want to buy one or not. And it may take weeks to get sorted out.
He'll inevitably feel that being without computer isn't so bad, so you start to say "can we actually sell a product during that downtime, or are you paying the salary of people who are just sitting on their thumbs?"