Use a multimeter to find out where there is a high resistance connection in power and ground (including the battery voltage itself, the connections at the battery, and thru the pos. jump post connections), or control signal. Do this by looking for a point of voltage drop under load of attempted start (ohming it with a standard multimeter doesn't tell you anything). Also inspect, disassemble, and thoroughly clean the connections at the battery and pos. and neg. jump posts. All of those are known common causes of your symptoms. If full voltage and ground to connections at starter and starter solenoid, then the starter or its solenoid are bad.
Starter power goes thru the jump post connections. The three cables coming together at the pos. jump post are (1) power from battery, (2) power to starter, and (3) power to everything else (except the connection between alternator and battery thru a dedicated wire including the green fusible link). Disassemble the pos. jump post, sand the cable terminal faces, and re-assemble making sure the nuts on the stud are *tight* - you need a wrench on both nuts torqueing against each other to do that. Be sure to disconnect top cable from neg. jump post before putting any wrenches to pos. jump post - if you don't disconnect that ground and wrench touches any surrounding metal while on the pos. jump post, there'll be lots of sparks, and possible damage or injury to yourself.
Corrosion at the battery post connections is a common cause.
Unlikely, but it's always possible that the new starter is bad, especially if aftermarket.
'98 LXi - Later Concorde gages (black w/ chrome rings)/'99 LX - LHS gages (white) - HIR bulbs
Last edited by peva; 12-14-2016 at 02:32 AM.