As per the description above, you want to download the Adobe ExportPDF service on your new laptop, Is that correct?
Adobe ExportPDF service is an online service and cannot be downloaded as an application. But we can access the services through a browser and can be accessed through desktop and mobile app Adobe Reader DC.
Access the service through the URL https://cloud.acrobat.com/exportpdf with your Adobe ID and password.
You can also use the free desktop version of Adobe Reader to use the service of Adobe ExportPDF, sign in with your Adobe ID and password in Adobe Reader. To download the Reader use the following URL Adobe - Adobe Acrobat Reader DC Distribution
For any troubleshooting, you may refer to Troubleshooting Create PDF, Export PDF, Adobe Send, Fill & Sign … services(PDFPack or Document Cloud...
Hope this helps, and let us know if you need more assistance.