You could pull the starter off and bench test it, but it's not very likely that it's the starter. It seems the problem is probably in one of your battery cables. When you jump start it, what happens if you move the negative jumper cable to a chassis or engine ground (like the alternator bracket)?
Probably a dumb question, but are your terminals tightened down on the battery?
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1989 7MGTE R154 Targa Top White Package w/Blue Interior
Driftmotion 57trim CT26, Upgraded Intercooler, 2.25" Hard Pipes, 3" Turbo Back Exhaust with Test Pipe, HKS VPC w/GM 3 bar MAP sensor, APEXi S-AFC, Walbro 255lph fuel pump, ProSport EVO Series Boost / Fuel Pressure / AFR gauges, Lotek a Pillar Gauge Pod, HKS Type 0 Turbo Timer, Eibach Lowering Springs, Tokico Illumina II TEMS struts, custom powder coated Motegi Racing TrakLite wheels
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