Desoldering from a graphics card
As part of your problem (along with ground and power planes sucking heat away from the joint), your solder may well be lead based, and the solder on the graphics card is almost certainly lead-free (everything in the last few years has moved to lead-free solders). The lead-free solders require significantly higher temps to melt than older lead-based solders. 

Unfortunately, I think the basic problem is that your iron is just not up to the task. The pre-heat trick might help, but I'd recommend just getting an iron that's got more punch.