If your chain command fails you use the Open door policy. Get on that VPs calender even if its for 10 minutes. Be very prepared for that 10 min meeting so you don't get sidetracked by pleasantries or talking about the weather or sports. Dont go into too much detail but stay at a high level talk about the problem and how it can be resolved. If a resolution will save the company money or affect the bottom line be prepared to state a number. After that short meeting they should decide if they want to discuss more and will set up another followup meeting.
If that fails, ambush them. Get close to their Admin and see where and when they will be. Most of the times VPs tend to get early or late hours at the office and that's the perfect time to knock on the door.
Lastly, and this is the most important, make sure you have exhausted all middle management routes. Why? That VP will ask who you have told or informed. You might see this as 'throwing those middle managers under the bus' but if the cause is worth it so be it. (just don't gloat, just say succinctly, I have told this person, and this person, and this person, etc. No other commentary about them should be needed.)
I actually have a good manager and has in the past said to issues that I have raised have said "Well, lets go meet the VP and/or the CIO." He really is a great manager. I have messed up from time to time but his reaction is one of the best ones I haven't seen since being in the military and that's, "What have you learned from this and how are you going to ensure that this wont happen again?" Also my company actually has a way to get things like issues moved up the chain. We have a monthly forum where issues can be raised and the convening board is all of the VPs from all of the business areas from within the company so nothing is swept away. (You submit to an email address first and the board convenes every three weeks to review submissions and then once a month for a Open forum.) Once raised the board asks that individual to come and present, asks questions, then decides how to move forward. Sometimes if the 'issue' is large enough that employee may get a monetary spot award.
However you proceed I wish you luck.