License allows 2 activations... DE-activate on old computer before installing on new computer if you will never use the old computer again
More information is necessary to give you an answer that applies to your specific situation.
1. What version of Premiere Elements is involved and on what computer operating system is it running now and on what computer operating system will it be running on the second (new) computer?
2. How did you set up your first computer....purchased online download from Adobe to Window 7 64 bit, followed by install there OR installation from Premiere Elements installation disc purchased in box packaging?
True, Adobe allows a purchased serial number for a given version to be activated on no more than 2 of your computers.
That is a critical consideration. But in itself that becomes moot if other factors do not fall into place.
Looking forward to your follow up details.