This kinda troubleshooting is tedious but, if you enjoy a challenge it can be a great opportunity to learn so hang in there. Not sure how far you want to go but I'll offer some things too, do what you will, I know you have a life
BTW, does your patient have a model number (sorry if I missed it), maybe a second pair of (not so tired) eyes can double check the drivers - but it's always good to provide such details anyway?
If you have room on a USB stick, in a separate folder (from downloaded drivers, etc) to keep things orderly, a helpful free portable tool is HWiNFO - Free Download HWiNFO Sofware | Installer & Portable for Windows, DOS
- it should provide details about your patient should you need some help. If you should try it grab the Portable for Windows 32/64 bit version. Don't get tricked by the LanSweeper download link, hover over the second green download link, you should see links to Fosshub, Local, FTP - for me I use Local (US). It will be a .zip file, when extracted you should see 32-bit & 64-bit versions - 32-bit (32-bit OS), 64-bit (64-bit OS). If you check Save Preferences in Settings I believe a .ini file is created.
Speaking of Device Manager, for your Audio (Sound) and Network adapters, if you click on Properties-General tab, are these devices Working Properly? Where does the Driver-Driver-Details tab point?
Does the Network adapter(s) have a Power Management Tab? Can the computer turn off the device? I would uncheck this setting for now. I would disable then re-enable the adapter.
If you can't get this to work an option is a USB WIFI dongle... I use the Edimax EW-7811Un. These are very handy to have when an internal NIC is acting up, making it hard to connect to the internet. You'll need an available USB port of course
Speaking of Audio... have you double checked to make sure you've selected the correct playback device? Right-click the speaker icon, rumage thru the various settings -> Playback devices and Volume control options. Make sure in Playback you have the correct device configured & tested, you said the owner was using a SMART TV too - uncheck any device not connected, that cannot provide a speaker system and setup (configure a device that can provide speakers).
Make sure Headphones weren't used via jack audio settings, and bypassed laptop speakers. You generally have the option to use external laptop speakers (suck bad), maybe TV (2nd display) speakers via HDMI, or plugging in a set of external speakers via the headphone jack??? I have all 3 options but I need to make a few changes in the audio settings. If I select the TV as the audio out source but don't turn the TV on I get no sound. I have decide to stick with using a modest set of external powered speakers connected via the 3.5mm headphone jack on my laptop, tweaked some by the HD audio drivers, as well configured as the default audio device. Point is it can get confusing when you need to figure out what someone else has done, what they may have checked or unchecked.
Another option you have, simply to bypass the Windows OS issues (drivers, settings, etc), is to create a Linux Live OS (bootable USB). This is one way to see if the hardware might be an issue. This will atleast let you know if the hardware is functional, or even worth bothering with at this point. A 13 year old laptop is lagging technologically speaking, even worse if you can't get the (Windows) drivers to make it work. Should you run this laptop thru its paces via a Linux distro, an OS less demanding hardware-wise than Windows, you might suggest to the owner if he/she wishes to keep the hardware, have a look at a Linux distro.
BTW, running a Live session from USB will effect this laptop nada, you can simply have a look at how it runs (performs), again, it may not even be worth the headache... but I honestly believe the process for you is a great learning opportunity should you continue troubleshooting.
After-thought. I hope the owner gave you the power adapter (cord)? If so, use AC power, a bad battery and some funky low power settings can cause problems. If possible, yank the battery and use AC power while trying to get your patient healthy