Generally speaking, DNA is relatively stable for long periods of time, even when isolated from a living organism. Isolated DNA does not need refrigeration to be maintained, however the rate of degradation can be further slowed by maintenance at low temperatures. Extreme conditions could prevent the DNA from being maintained, so the condition of the corpse is critical to answering this question accurately.
Assuming that the DNA is stable, then any mitochondrial disorder which has defined genomic characterization should be identifiable after death. Whether or not this can be done in a corpse ofter a year old probably depends on how the corpse was stored during that year, and the state of the DNA. Biochemical disorders which have known genetic basis (in other words, if you know the gene which causes the disease) should be identifiable based on sequencing the DNA and confirming the presence or absence of sequence mutations.
Using histology slides to identify diseases generally means that you are looking for the presence of proteins which are markers of a disease. First, the tissue would have to be preserved. This could mean that a sample was taken when the corpse was fresh and stored in preservative for a year, or that the corpse was frozen during that time. Assuming that the cells and tissues are intact, you would then need to know what proteins are associated with this disease. If you know this, you can hybridize the tissue sample with an antibody conjugated to a stain. This is usually done by creating very thin slices of tissue (normally embedded in paraffin wax) and fixing them to histology slides. These slides can then be hybridized to your stain/antibody conjugate and viewed under a microscope. The presence of stain indicates the presence of your protein.