parismountain -- not dumb at all. It's actually really complicated -- so this will be only mostly correct, but should clarify a bit, hopefully. I'll be really broad, because I don't know your background at all, and this is sort of a connection point for a lot of biology, so I want to try to give you something better than yes/no.
Once something like a retrovirus incorporates its genome into that of a host cell -- it's then called a provirus -- it will be present in every daughter cell that comes from that host cell. If one cell in my big toe gets infected with Virus X that incorporates into its DNA, then every cell that comes from the splitting of that big toe cell will also have that (currently latent) provirus. If the virus is active in another cell, it will be using the machinery of the cell to pump out new copies of the virus, too. Other uninfected big toe cells will still also be dividing, so everything is happening at once -- infected cell may be splitting off into more infected cells, uninfected cells may be splitting into more uninfected cells, and active viruses may be running around infecting more cells. It's more of a balance than of a yes/no, and the reaction of your immune system makes a huge difference in trying to tip that balance toward healthy cells.
With white blood cells specifically, they don't really divide directly from each other, though. They're produced from stem cells in your bone marrow, and once they differentiate into whatever kind of blood cell they're going to be, they generally lose the ability to self-replicate; the bone marrow keeps pumping out new ones as the old ones die off. Now, if your stem cells have the provirus, then so will the blood cells they produce.
Add to that mishmash that we have systems designed to kill cells that have irregularities in their DNA -- the cell itself is set up to have a number of ways it may either stop replicating or kill itself if its DNA is really damaged, and there are other cells out there on the lookout for signs of infected or damaged cells, which they will then kill. In something like HIV, for example, the CD-4 cell depletion happens in part because one's own body attacks the infected CD-4 cells. Again, gets way more complicated than that, but that's sort of the basic picture.
Damage to DNA -- whatever the source, viruses are just one -- will most often result in the death of the damaged cell, but if it doesn't, and it's an actively replicating cell, then that cell is replicating into more cells with that damage. Damage to some regions can lead to tumors this way, if the cell has damage, say, to the parts that tell it <i>not</i> to divide all willy-nilly. If it neither kills itself nor is killed by other cells, it will become a big lump of dividing whatnot. This is why we have systems for autoimmunity, which can also sometimes sadly go awry and kill perfectly healthy cells.
It's really an oversimplification to say that every cell in your body has exactly the same genetic information. Sometimes, there are mistakes in transcription when cells divide, and sometimes cells sustain damage of various kinds that create small mistakes somewhere in the code. Cells do have mechanisms to try to repair these mistakes, but that's not perfect, either, and some may remain from time to time. Most of these are harmless and tiny, and aren't noteworthy at all when you're talking about looking across your whole genome, which is huge. When there's a change that is large enough or well-placed enough to be harmful, your body actively tries to kill the cell (if it won't kill itself).
If these mutations happen and survive in most types of your body cells, they're not generally a big deal, and they're so small as to be insignificant for something like DNA sequencing -- they will still all be 99.999999% alike or whatever. If changes happen to the DNA in the cells that make eggs or sperm, they will be passed on to your children, should you have any, as mutations that will be in <i>all</i> of their DNA. Random mutations aren't uncommon, they increase in cells over time (this is part of aging, really), they're usually completely meaningless, and when they aren't, they're the fundamental stuff of evolution.
Whew. Hope that wasn't too far afield and that I actually answered your question in there somewhere.
