Sigh. MrDEB, I truly wish you could post a message with pertinent details that can be comprehended by mere mortals such as myself.
In the paragraph above, you talk about PICkit calibration, internal oscillator settings and etc and say "it doesn't work." From that statement, nobody can know what "it" is.
Questions. A clear, concise answer is required to each before I will do anything further to help you.
1. Did you run the Vdd calibration procedure under the PICkit 2 GUI?
2. When you attempt to write to the 18F13k22 chip, does it complete satisfactorily or is there an error message displayed? If so, post screen captures of the PICkit 2 GUI and of the error message.
3. Did you verify the code was written correctly to the 18F13K22? It's an option under the PICkit 2 GUI.
4. If and only if the code was written into the 18F13K22, how do you know it's not working? Simplest possible program. Post code and schematic diagrams in a clear readable format. I'm not going to guess at what you're doing or assume you have correct connections. Sorry, past performance suggests to do so is foolish.
5. If the internal oscillator code isn't working (post your actual code), and the chip is actually being programmed (verified in the PICkit 2 GUI), try it with a crystal and 22 pF caps.
Sorry to be blunt, but if you want help, you need to post all of the details clearly and concisely with appropriate documentation posted. Many of us have been burned in the past by making assumptions about what you are asking, or assuming schematics actually show what you have connected.
I do not believe the 18F13K22 chip should be any more difficult than any other 18F chip to use, but as always, attention to detail and the data sheet will be required.