Import Data To Table With Foreign Key Triggers

I've imported data from an Excel spreadsheet to a table that has fields to match the destination table I'm trying to populate. The destination table has an Insert trigger with several checks on certain fields to make sure they have corresponding records in other tables.

If I do a statement like
"INSERT INTO destinationTable
(
ItemId,
Product,
SuperID,
etc etc
)
SELECT * FROM oldtable"
it runs for a while then gives me error messages from the trigger and rolls back the Insert.

The trigger has code such as
"IF (SELECT COUNT(*) FROM inserted WHERE ((inserted.Product Is Not Null))) != (SELECT COUNT(*) FROM tblInProduct, inserted WHERE (tblInProduct.Product = inserted.Product))
BEGIN
(Error message code goes here)
END"

So, do I need to do an INNER JOIN to each of the related files?
When I try that, I get this error:
"Msg 121, Level 15, State 1, Line 2
The select list for the INSERT statement contains more items than the insert list. The number of SELECT values must match the number of INSERT columns."
Is SQL counting the foreign key fields as separate fields, or what?