Do you need an autopsy to be cremated?
No, but depending on the circumstances surrounding the death, an autopsy can be ordered by a coroner. In many jurisdictions, autopsies are required for people 45 years and younger. in some, 50 years, and in a few 55.
Insofar as cremation, once the initial investigation into ones death has been concluded (an autopsy may or may not have been performed) and an official cause of death has been certified by the attending physician/coroner, the body will be released, to next of kin for disposition. It is at that point when the decision for burial or cremation is determined.
In the UK the procedure is as above, but if the death was in an accident or suspicious circumstances - the coroner's court must become involved. An autopsy does not have to take place, but often it will be to determine how the death occurred. If a body part is essential to the coroner's hearing - these body parts may be temporarily retained for investigation after consultation with the next of kin.
In such cicumstances the coroners court will give direction as to whether it is appropriate for the body at that stage to be cremated as there maybe an issue of reconciling the body parts with the rest of the body.
Can an autopsy be performed 4 years after a person has been cremated in a very sealed box in the ground?
In general, an autopsy cannot be performed at any time after a cremation. During cremation, soft tissue is totally detroyed by heat. Remaining bone fragments are reduced to a powder. While a limited number of forensic test may be made on the bone fragments, there is simply no body on which to conduct a post mortem exam.
Virtual autopsy, aka post-mortem-imaging is performed around the world to reduce the need for a standard autopsy, but also to add precision in the reporting and preparing the standard autopsy. For solutions see for example Sectra Visualization Table, http://www.sectra.com/medical/radiology_it/offering/visualization_table/forensics/index.html