What is the "problem" you want to solve?

If you want a statement about whether or not the gene (mRNA) is expressed, you have it (I assume the CQ value is obtained from a specific amplification signal). If you want a quantification, you will likely require large sample sizes to get a sufficient precision (and a censoring model to account for "non-detects").

Cq values tell you

A) whether it's there or not

B) if there, how much of it is there

Here, the answers appear to be "yes" and "almost none". So from this you can then make value judgements regarding biological context.

If this is a homogeneous population of cells, then I would be inclined to ascribe this to random stochastic noise (it simply isn't possible to suppress genes 100%, so you often get some random bursts of expression).

If this is a mixed population of cells, then this could be of biological relevance: what you could be seeing is "high expression, but in a very small number of cells" (for example, one or two early-stage activated T-cells in a mixed PBMC prep might give you low but detectable markers of activation).

You haven't really provided enough detail to answer your question more fully.

Hello Mu Mu,

As usual, a lot of critical info is missing in the question: which system are you using for qPCR: SYBR-green, TaqMan ..., what is your template, gDNA, mRNAs, miRNAs, lncRNAs, are you expecting a yes/no answer, absolute quantification or relative quantification from your qPCR ... What negative controls are you using? NTC only, or -RT or in the case of gDNA, gDNA from an unrelated species? How do your melt curves look like and how are the CTs of your technical replicates... All this info would help to give more specific answers.

Theoretically, if your negative controls don´t produce any product, and if your technical replicates are consistent (less than 5% deviation, depends on the accuracy of your pipette), the melt curves give a clean and single peak, you would be able to say that the product is not an artifact. You could even sequence it to confirm specificity. However, what will be more important: you´ll need some functional assay to test whether whatever you were checking has a biological effect. It´ll not matter how big or statistically significant differences are unless a biological function can be shown.

One thing about negative controls: NTC is a bit of a cheater. It only accounts for primer dimers and contamination of your reagents with target DNA/cDNA, so it should of course be included. However, if you work with cDNA, -RT controls are even more important as they´ll allow you to judge whether there are traces of gDNA left that produce either specific or spurious PCR products. Even with intron-spanning primers, you might get some spurious PCR products, so having the "right" size is not absolute proof.

Let's pretend for the moment that we are dealing with detecting a deadly pathogen. Let us also assume that you have proven by melt curve analysis or by direct sequencing that one of your samples with a Cq >35 indeed shows that your amplified product is indeed the pathogen target sequence. Reactions with a starting single copy of target sequence have been reported to appear anywhere from Cq of 35 to 38 in highly efficient qPCR reactions, whereas a Cq of 48 (proving to be a real target amplification) in a 70% efficient qPCR reaction is entirely possible (and has been demonstrated). So Otilia and Sachin's comments above are very informative in this regard.

In rough language, a Cq range of ~14 to 38 is most useful in qPCR. But, if primer-dimers and non-specific products start showing up at, say, a Cq of 28, the qPCR starts to be questionable at a Cq of >=28. Like the others have mentioned above, if you have unequivocal proof that your high Cq values are indeed amplifications of your specific intended target sequence, then, they are real and useful measurements. Proof of fidelity for target in reactions yielding high Cq values is a must.  Also, if indeed a Cq of 48 (in a poorly efficient qPCReaction) proved to be the target sequence for, e.g., Ebola, one can make a strong case for not throwing the baby out with the bathwater as it were.  Proof by direct sequencing or good melt curve analysis of the product is a must in these situations.