You need something like this.
https://www.amazon.com/Small-PCB-Slimline-Slim-50-Pin-Adapter/dp/B003NVTDCO
Search for slim atapi or slim50 ide, and add whatever interface you want to convert to, ex. ide, usb or sata.
Make sure it's the drive itself, not the adapter. I have a 2GB HDD that works perfectly on the Toshiba but no other computer sees it with my USB adapter, though it still works for other drives (including the CFs).
To use a CF with the Toshiba, I bought this: http://www.dx.com/p/compactflash-cf-card-to-ide-hard-disk-adapter-card-ide-44-10310
You'll need to cut off or bend away the key pin located on the back side of the PCB however, where the IDE connector in the Toshiba doesn't have a hole. (Mechanical HDDs have that missing pin as well, so you can use that to check, too.)
Trackball might have some dirt on the rollers or rotary encoders so it can't see left/right movement. Can you remove the ball and clean inside?
Also, no idea what that laptop is, but with less than 8MB of ram i doubt there are many linux distros you could run. Even http://www.damnsmalllinux.org/ which is based on an ancient Linux kernel needs more RAM than that.
You can run DOS software from Windows 95, but that might not give you true information. Some things are virtualized when running under Windows. But you can restart the computer in "DOS mode". Or you can make a shortcut to DOS program that automatically restarts in "DOS mode". You can also try pressing "F8" while booting to get to Windows 95 boot menu and choosing "DOS mode" there.
HWiNFo32 (Windows version) used to work on Win 95 few years ago. But I'm not sure if that's still the case.
Does it have a CD drive, or do you have the option to boot from USB? If so, you could just download a copy of DBAN (https://dban.org), burn to disc/create bootable USB, and run that. Alternatively, download any Linux "live" distro, boot it up, and you can then use the dd command to zero the drive - there are lots of guides on the internet that explain how to do this.
Unfortunately, HP won't provide any drivers pre-XP. You could try a site like DriversCollection.com - however, be warned that these sites can be a source of viruses, malware, and other nasties.
https://driverscollection.com/?H=Compaq%20Presario%202266&By=HP matches what you are looking for, and has a copy of the graphics driver for that machine (SIS chipset).
I've just downloaded the installer (sp8813.exe) into my sandbox VM, and Malwarebytes Premium reports it as clean, however that's no guarantee it is safe to use. It appears to be a genuine SoftPaq file (So looks like it actually came from Compaq themselves). The INF file in the installer is for "SIS 5597/5598 display driver", and a bit of Googling shows this machine used the 5598 chipset, so should be good. It targets Windows 95, but Windows 98 often used drivers from 95.
It's up to you really - there's always a risk that using 3rd party websites to obtain drivers could result in infection. If you feel the risk is too great, you could clone the hard disk that contains the important data, that way you can still put the original drive to one side, and instead use the cloned version. Clonezilla (https://clonezilla.org) is open source, and extremely good.