There is no way to for users to control the 2010 install/activation count.
As long as it is a "retail" / "FPP" Office license, the number of computers sequentially is not limited in theory, just the number at the same time.
Since you are mentioning 4th computer, I'll guess that it is Home and Student, which allowed install on up to 3 computers at the same time.
As long as that Office license has been uninstalled from one of the other computers, freeing up an "install count", you can do the install on the "4th" computer.
If internet activation does not work, do phone activation. Let us know if you get any error messages. Most of them seem real, but are not!