What percent of cases of deep vein thrombosis are caused by an undiagnosed chronic viral infection?

This is almost entirely viral in origin, on the order of 98% of cases. So it is the major predisposing factor. Not all sites of injury or invasion will lead to as dramatic a coagulation problem, with subsequent widespread injury and even potential loss of function or death from pulmonary embolism, for example, as a consequence of heavy clotting in the vessels.