my 1998 suburban doesnt crank but everything else works and the security light flashes

i just recently bought a 1998 GMC suburban. it used to start up fine then it
would take a few cranks for it to start up now it doesnt even engage the
starter. i replaced the starter only to find that my original starter was good. i
replaced the battery and gave it a tune up. when i insert the key and try to
crank it (crickets) nothing happens. the lights, power windows, door locks
horn, radio evrything works but it doesn't crank at all . the security light on the
dash board blinks when the key is in the on position and turns off when i
remove the key. i purchased an EVO all bypass module and found out it won't
bypass the oem security system it only bypasses the remote start module can
some please...HEEEEEELLLLPPPPPP!!!!!!!!!