Hello Eyes-Wide-Open,
I understand you are having sound issues where the sound cuts out after 10 minutes, you also noticed a build up of dust or crud in your Notebook. I am recommending that you review and follow the steps in the HP Support document: Reducing Heat Inside the PC to Prevent Overheating as the build up of dust or crud can lead to this and it can affect your computer is a variety of ways.
If the sound issue persists after you have followed the steps I would encourage you to post which operating system you are using. And whether your operating system is 32-bit or 64-bit as with this we can provide you with accurate information.
Which Windows operating system am I running?
Is the Windows Version on My Computer 32-bit or 64-bit?
Please re-post with the requested information and I would be happy to provide you with assistance. Thank you for posting on the HP Forums. Have a great day!