No DNA detected IS a test result, yes, absolutely.
If there was an inadequate sample, the report would have said so.
If a blood antibody test is done too soon after a new infection, it could be falsely negative. It takes time to make antibodies, some people take longer than others. If you follow this up say in 6 to 8 weeks with another IgG test and it is boldly positive then I think that does represent a new infection. Remember that the IgG test can have false positives so I would be really careful about continuing to use that test.
Terri