Good day!!
Well, I just so happen to have done door lock maintenance on my new-to-me 2004 (that I will be posting info about in another thread)... If your key looks like mine, it has a channel down the center of the flats... This channel moves the tumblers until the key is all the way in... Once in, it should have all the tumblers even with the barrel... Thus being able to turn it... There are springs that keep the tumblers at the extreme limit (and will force the tumbler out if not assembled in the lock barrel)... You might have some broken springs, damaged lock tumblers, or worn out key...
This is my door lock tumbler, but it probably has the same set-up for the ignition... Which would also indicate it is the ignition lock if you don't have any issues getting into the car with the key... It's the key if the door lock has the same issue...
This also has a grease type stuff on it... So, I don't think any kind of grease you use would be wrong...
Good luck!!
Cheers!!