Ah ok. It's actually your where clause that is causing this. If you need to treat each skill individually, for purposes of filtering the query and pulling back people, you're going to need to change all those ANDs to ORs in your where clause. Basically, that where clause says "only give me people who have anything but zero in ALL columns"
Try this:
SELECT tblWorkArea.ID_LaborCore ,
tblWorkArea.[Labor Core] ,
tblWorkArea.Position ,
tblSkills.[Reading Schematics] ,
tblSkills.Wiring ,
tblSkills.[Wire Type] ,
tblSkills.[Terminal Types] ,
tblSkills.[NEMA Ratings] ,
tblSkills.[UL 508] ,
tblSkills.[Attention to Detail] ,
tblSkills.[Lifting 50lbs] ,
tblSkills.[Knowledge of Procedure] ,
tblSkills.Crimper ,
tblSkills.[Heat Gun] ,
tblSkills.Screwdriver ,
tblSkills.Stripper ,
tblSkills.[Impact Drill] ,
tblSkills.[Radial Saw] ,
tblSkills.Multimeter ,
tblSkills.[Torque Screwdriver/Wrench] ,
tblSkills.[Tape Measure] ,
tblSkills.Vacuum ,
tblSkills.[Drill Press] ,
tblSkills.[Jig Saw] ,
tblSkills.[Troubleshooting Components] ,
tblSkills.[Problem Solving] ,
tblSkills.Organization ,
tblSkills.[Large Panel] ,
tblSkills.[Test Procedures] ,
tblSkills.[Functional Testing] ,
tblSkills.[Writing Test Procedures] ,
tblSkills.[Material Management] ,
tblSkills.[Set Meter Ability] ,
tblSkills.[Tone Generator] ,
tblSkills.[Megger Testing] ,
tblSkills.[Network Tracer] ,
tblSkills.Components ,
tblSkills.Fuses ,
tblSkills.[Heat Shrink Color Codes] ,
tblSkills.[Proper Lug or Crimping] ,
tblSkills.[Resistors Knowledge] ,
tblSkills.Oscilloscopes ,
tblSkills.Waveforms ,
tblSkills.[Voltage Separation] ,
tblSkills.[Skill x_Stapling]
FROM ( tblWorkArea
INNER JOIN tblPosition ON tblWorkArea.Position = tblPosition.Postion
)
INNER JOIN tblSkills ON tblWorkArea.ID_LaborCore = tblSkills.ID_LaborCore
WHERE ( ( ( tblWorkArea.[Labor Core] ) = [Enter labor core] )
AND ( ( tblWorkArea.Position ) = [Enter Position] )
AND ( ( ( tblSkills.[Reading Schematics] ) <> 0 )
OR ( ( tblSkills.Wiring ) <> 0 )
OR ( ( tblSkills.[Wire Type] ) <> 0 )
OR ( ( tblSkills.[Terminal Types] ) <> 0 )
OR ( ( tblSkills.[NEMA Ratings] ) <> 0 )
OR ( ( tblSkills.[UL 508] ) <> 0 )
OR ( ( tblSkills.[Attention to Detail] ) <> 0 )
OR ( ( tblSkills.[Lifting 50lbs] ) <> 0 )
OR ( ( tblSkills.[Knowledge of Procedure] ) <> 0 )
OR ( ( tblSkills.Crimper ) <> 0 )
OR ( ( tblSkills.[Heat Gun] ) <> 0 )
OR ( ( tblSkills.Screwdriver ) <> 0 )
OR ( ( tblSkills.Stripper ) <> 0 )
OR ( ( tblSkills.[Impact Drill] ) <> 0 )
OR ( ( tblSkills.[Radial Saw] ) <> 0 )
OR ( ( tblSkills.Multimeter ) <> 0 )
OR ( ( tblSkills.[Torque Screwdriver/Wrench] ) <> 0 )
OR ( ( tblSkills.[Tape Measure] ) <> 0 )
OR ( ( tblSkills.Vacuum ) <> 0 )
OR ( ( tblSkills.[Drill Press] ) <> 0 )
OR ( ( tblSkills.[Jig Saw] ) <> 0 )
OR ( ( tblSkills.[Troubleshooting Components] ) <> 0 )
OR ( ( tblSkills.[Problem Solving] ) <> 0 )
OR ( ( tblSkills.Organization ) <> 0 )
OR ( ( tblSkills.[Large Panel] ) <> 0 )
OR ( ( tblSkills.[Test Procedures] ) <> 0 )
OR ( ( tblSkills.[Functional Testing] ) <> 0 )
OR ( ( tblSkills.[Writing Test Procedures] ) <> 0 )
OR ( ( tblSkills.[Material Management] ) <> 0 )
OR ( ( tblSkills.[Set Meter Ability] ) <> 0 )
OR ( ( tblSkills.[Tone Generator] ) <> 0 )
OR ( ( tblSkills.[Megger Testing] ) <> 0 )
OR ( ( tblSkills.[Network Tracer] ) <> 0 )
OR ( ( tblSkills.Components ) <> 0 )
OR ( ( tblSkills.Fuses ) <> 0 )
OR ( ( tblSkills.[Heat Shrink Color Codes] ) <> 0 )
OR ( ( tblSkills.[Proper Lug or Crimping] ) <> 0 )
OR ( ( tblSkills.[Resistors Knowledge] ) <> 0 )
OR ( ( tblSkills.Oscilloscopes ) <> 0 )
OR ( ( tblSkills.Waveforms ) <> 0 )
OR ( ( tblSkills.[Voltage Separation] ) <> 0 )
OR ( ( tblSkills.[Skill x_Stapling] ) <> 0 )
)
)