No, you can install your license on the new PC as long as they are compatible (e.g., if your year of QB is supported on the OS of the new PC).
Resolution for 'Quickbooks issue: 'If my PC dies, do I have to buy another copy of Desktop Pro?' available: Yes.
The Quickbooks issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the Quickbooks issue yourself by looking for a resolution described in the article. If it is a complex Quickbooks issue or you are unable to solve the issue, you may contact us by clicking here or by using other Quickbooks support options.
For more information about resolving issues related to Quickbooks in Quickbooks/QBO or to get support for the issue 'If my PC dies, do I have to buy another copy of Desktop Pro?', click the link below: