Deactivated dead computer and activating the other "no subscription" when the laptop version is on.

Are you trying to sign in to Photoshop or the Creative Cloud app? It's the CC app you need to log on to first.  In fact, I thought you fave to signed in to even download a CC app.  So, to clarify, are you able to sign in to the Creative Cloud app?

Contact Adobe Support and ask them for an activation count reset for your legacy product.  If necessary, ask to speak with a supervisor as most new hires won't know what you're talking about.  DO NOT ask for anything more than a count reset. Adobe can't help you with discontinued software.

Online Chat: https://helpx.adobe.com/contact.html?rghtup=autoOpen
Twitter: https://twitter.com/adobecare

That said, 10+ year old software must be replaced at some point.  You can't keep using it forever.  New equipment requires new compatible software.

MODERN OPTIONS:
Photoshop Elements or Premiere Elements (approx $100, no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Camera Raw
• Lightroom on desktop, mobile and the web
• Lightroom Classic
• Portfolio website + hosting
• Adobe Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).
• Free upgrades for paid subscribers

https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (20+ pro apps & services) and Single App Plans
https://www.adobe.com/creativecloud/plans.html

Hope that helps.