So, the first issue (detection) comes down to the detection of a target gene at some minimal level using polymerase chain reaction or perhaps an enzyme-binding assay or something like that. These molecular biology techniques can actually detect even a few copies of a gene (i.e. a virus) in a sample tube, so a finger prick could plausibly work for this kind of detection goal. The main thing to keep in mind is the difficultly of quantitative measurements at these low levels. For example, I wouldn't be easily able to tell if my sample had ten copies of the gene or a hundred copies of the gene, certainly not cheaply and efficiently.
But, the blood chemistry tests - the second, quantitative goal - are far worse. Those are supposed to produce results with error bars, I'd guess at least +/- 10% accuracy is what you want (I'm not a doctor or nurse). But if you have a finger prick, well, what about evaporation of liquid volume? You can see it happening on a really good scale, 10 ul will evaporate away pretty fast. Also, is a finger prick (capillary) going to be like blood from a vein?
The problem is that precision with tiny volumes is possible, but requires massive preparation and dedicated professionals and certainly doesn't scale easily. Any such system would have to be calibrated daily, tested (with known standards), then samples would be run, then you test it again... Let alone cross contamination and about a hundred other problems. Furthermore - 26 different quantitative tests at once???
So, that's the kind of thing I meant when talking about the easier detection goal (where 26 pos/neg 'is the gene there' tests on a single sample might be plausible) vs. the much harder quantitative goal.