Hi ! Sorry to have taken so long to give you a reply, I'm up to my armpits in unread posts at the moment.
I know that current emission standards for modern computer monitors is partly if not largely as a result of research done on the early VDU operators, as Data Input Operatives were then called. (Basically, anyone who sat in front of a monitor all day.)
The majority of these people were women and distinct serious health effects were discovered, to a degree that was not in any way doubtful. Unfortunately I cannot remember all of them, nor can I remember any of the researchers - I read all this donkey's years ago - but the main one that caused alarm was a greatly increased level of fetal abnormalitites. Many more cases of stillbirth, miscarriages, and teratogeny (malformed fetuses) were statistically linked to the amount of time spent in front of a VDU. I believe that the other health concerns were regarding leukaemia and immune system abnormalities - but I wouldn't like to say I'm sure of that. Anyway, as a result, much stricter limits on the electromagnetic emissions put out by all Cathode Ray Tubes were legislated, as well as limits on the amount of time and proximity allowed for pregnant women working on or near VDUs. (It was this legislation that started the recommendation that people should get up and take frequent breaks, move about etc, and that pregnant women should undertake non-VDU duties if working in the earlier trimesters.)
The amount of non-ionising radiation we are currently exposed to from these sources is much smaller now than then - the Energy Star efficiency program for monitors helped in this - and so I wouldn't be too concerned nowadays. By comparison the health implications of frequent mobile phone use, living near to a mobile phone mast or underneath high-voltage power lines, is more likely to be severe, although that supposition is as far as I know still very open to debate. (The Swedes are leading the way in this field, if you want to do a google search on non-ionising radiation.)
In case you don't already know, non-ionising radiation is very different from radioactive radiation. The two things are very different creatures; the only reason they are both called radiation is that they both come from a point source and decrease in strength according to the inverse square law. (In other words, like the heat from a fire - which is also a form of radiation - if you are twice the distance away, you get one fourth of the effects, four times as far away, one sixteenth.)According to what I've read, TVs do give off an appreciable amount of radiation if you sit close enough to them - I think it is something like a metre - so small children parking themselves right in front of it is a bad idea. For the rest of us however watching TV from the usual distance of a couple of yards, is going to give us less of a dose of radiation than we can get from reading a glossy magazine.
I hope this helps clear things up....frankly, when it comes to CFS, I'd be inclined to look for neurological/pathogenic/chemical causes before I'd suspect any form of everyday radiation absorbed in typical doses.