Hard starting 2005
 

My 2005 Mini Cooper cranks but doesn't fire. If you let it pump by turning it to on a few times before cranking then it does fire. It seems like a failed fuel pressure check valve that is leaking down.

Has anybody had this? Is it a fuel pump problem or a fuel pressure regulator problem? I'm not sure where the check valves are.

This car sat on a car lot for 5 years before I bought it today (35k miles) so it might be a rare problem related to my circumstance but I sure would appreciate any useful insight.

I'm pretty good at troubleshooting and repairing but this is my first Mini.