Aside from the question of a definitive biomarker, or biomarkers, there are suggested tests that may indicate abnormalities, but these are not of course recognized biomarkers of ME.
As others have said, there isn't a recognized biomarker for ME. Also as others here have said, exclusion of other diseases is important.
In my experience, after exclusion of all else, what was left for me was "cfs", or "Chronic Fatugue Syndrome", much later confirmed by an expert, who at that time used the term ME/CFS.
The ME expert looked at my tests that mirrored some results that other pwME had, noted my symptoms, did some more tests, and confirmed my diagnosis.
If a person's aim is to indicate there is some form of dysfunction or some level of disability, this might be a lower bar to meet.
Research has found abnormalities in some pwME. I would suggest the Canadian Consensus Criteria (CCC) for ME/CFS, and it's Overview. Page 18 of the Overview lists the tests ME experts have found to be abnormal in some pwME. The CCC was written by 11 ME experts who had seen 20,000 pwME by time of publication on 2003. The Overview came out in 2005, if I'm not mistaken.
This info can be found on the website for the ME/FM Action Network. I will add the link to these a bit later. MEpedia probably also has these documents.
As well, the 2015 Institute of Medicine report on ME/CFS has info on tests. I think MEpedia also has this document.