Which disease agent gets inside the host cell and uses the DNA of that cell to replicate?

Virus.

Explanation:

A virus is a disease agent that gets inside the host cell and uses the DNA of that cell to replicate, and create new viruses. This is done when the virus hijacks the host cell, and essentially forces the cell to replicate the viral genome, then producing proteins that will compose the virus's protein shell (capsid). Following the replication of the virus, the host cell will disintegrate (lysis), and the new viruses will depart to infect more host cells.

nope...

but thanks for the points though!