Cloning problem. Digestion test at the end of the cloning is always negative
Even minute amounts of undigested vector will contaminate your transformation. You could PCR amplify your insert from the pJet cloning plasmid and then digest the PCR product with BamHI and HindIII. In order to get rid of the pJet template either gel purify the digested insert, digest pJet with some times which cuts it multiple times (less preferable) or put everything on a column and hope that pJet is diluted enough (less time consuming but a bit risky).

The other thing you could exploit is that pJet is ampicillin resistant while your target vector is also Zeocin resistant. If you add Zeocin to your E. Coli it will kill a pJet positive clones while sparing the pSecTag positive clones.

Your insert is fairly small so using a bit more DNA than usual won't hurt.

If you can post some pictures of your gels this might be helpful as well.