Living in Leicester I suppose we should be grateful it's not DeMonfort University that are digging up the carpark,given their apparent desire to take over every possible piece of land in that area by building on it.
They (the archaeologists) might find traces of decayed organic materials like leather shoes or belts or other artefacts...from the 15th century using carbon-dating techniques (to verify the approximate decade/century)...but DNA identification of human remains ( and proving that they belong to King Richard III ) seem impossible [to me].
"They can get DNA from the bone marrow after a couple of thousand years."
Mitochondrial DNA has been extracted from the teeth of a man who died at least 9000 years ago. His skeleton was discovered in a cave in Cheddar in 1903, and scientists extracted the DNA 94 years later.