Why doesn't my hdmi cord go in the port?

Hi @gabefleming

Use a strong light and a magnifying glass to check if the pins in the HDMI port anad also the HDMI cable plug are all OK and not bent, broken or missing, preventing the plug from inserting into the port.

If the problem is with the PS3's HDMI port, it will need to be replaced as it cannot be repaired.

Here's a video that shows how it done. Here's the ifixit PlayStation 3のマザーボードの交換 guide that may help.

Replacement HDMI ports are available online. Search for PS3 HDMI port to find suppliers that suit you best.