No. Back in the day power supply units used to be external: the reason being that they were instantly swappable in situations just like yours.
If power’s getting to the card then something’s likely gone amiss on the PSU module – which’ll be near the IEC socket, but of course it’s inside the console. If it’s outside warranty and you’re brave enough you can open it up and take a look because it could be something obvious like an internal fuse. I’m not recommending this but it’s not out of the question. It’s VERY IMPORTANT to replace any blown fuse with EXACTLY the same one though (including F or T): fuses sometimes blow for mundane reasons, but more often because they’re protecting against more catastrophic damage.
