The key question was what was the state of the battery when you left it unused for 6 weeks. It should have been charged to 50% and turned off. If it was not turned off and the battery ran down below zero % for an extended period the battery is completely dead. Lithium batteries cannot tolerate being completely flat.
Charge it for 1 hour with the wall adapter. Then hold the HOME and SLEEP buttons at the same time until something happens. If nothing happens after holding for 1 minute, and you are sure the power source and the cable are OK (they work with other devices), your battery is not only dead, it is shorted, so you won't even be able to start the phone when plugged in.