If your NAC corresponds to the NO-RT.......Did you design your primer on 2 different exons or not? it could be that the DNAseI treatment was not 100% efficient and you are amplifying the genomic DNA.

In addition to Erika's excellent answer, if you are amplifying a highly-abundant reference (formerly "housekeeping") gene that is also present in the dust in the room in which you work (a large percentage of dust is sloughed human skin - and animal skin if working with animals as well), you may be amplifying that target in your samples if they got a small amount of dust in them and your primers are permissive because they were not designed with exon-exon junctions in mind. What target are you amplifying, and in what organism? But, more likely (along with non-exon-junction-spanning primers) would be Erika's answer. A Cq of 30 is fairly loud. Ribo18S contamination (from ambient dust) commonly appears between 34 and 38 cycles if inadvertently present (even when being very careful), and your problem signal is 'louder' than a usual level of 18S contamination. So, incomplete DNase treatment of carry-over gDNA would seem to be the problem (if faulty primer design permits).

The only other obvious possibility would be primer dimers if you are using a SYBR Green-based mastermix. Aggressive primer dimer formation can haunt a reaction as early as 28 cycles on occasion. Have you checked your melt curves for the presence of primer dimer?

Thank you for your various interesting suggestions. In fact, the problem was an insufficient treatment of DNase I.

I was told that this might depend on whether you are using a SYBERmix solution or a probe based method. Which one is it?

I used a SYBERmix solution. Can you develop your idea?

SYBR will detect any product, specific or not, including primer-dimer. If you use a target specific probe (Taqman etc) you will detect only the amplification of your target regardless of anything else that may be amplifying in your qPCR. Also, probe-based methods can easily be multiplexed.