So, my question is can a state, like Illinois which banned Rod Blagojevich from holding office in Illinois after his impeachment also ban that person from holding Federal office in that state, such as the House of Representatives or the U.S Senate?
If Blagojevich wanted to run for President in the future, would he be banned from appearing on the ballot in Illinois?
No.
The US Constitution sets exclusive qualifications for federal offices.
At best, Congress could expel an elected member who did not attend sessions because he was in prison.