They look like they have a decent return policy so it may be worth a try, and if you pay with paypal, you can file a dispute is worse comes to worst.
There are some alternatives such as g2a.com or /r/softwareswap, where you can get keys (not serial numbers but just keys) for about the same price. I got one on /r/softwareswap and I haven't had an issue with it.
About the crashing, I can't say whether it's because of the key or not. Never heard that invalid keys cause that, so I'd make sure that that is the problem and not a hardware or unrelated software issue.
/r/softwareswap doesn't allow Windows products anymore, there was a pretty huge rash of people abusing a glitch with the student DreamSpark system to get unlimited software keys, last I checked Windows products are banned.
This subreddit is for general discussion of computers.