0) The fact that it starts when you jump the starter is a sign there is
no problem with the starter or starter's solenoid.
1) Listen for a clicking noise when you turn the key.
2) If you hear one coming from under the dash then the starter relay is
receiving current but not making contact.
3) If no click, then it's either the ignition switch that is bad or more
likely, if you have a manual, the clutch pedal starter defeat switch.
4) To check that last possibility, turn the key to «start» and hold it
there but pump the clutch pedal «150 times...».
5) If it suddendly starts, you've found the culprit, it's just a case of
replacing the switch (sits on top of the clutch pedal stem) or, like I
did on my Legacy, soldering the two wires that go to the swith together
to bypass the switch.
6) I have no experience with bad ignition switch contacts.
Good luck,
Gilles, Montreal.