I'm sorry for your frustrations, yes, computers can do that.
Im not HP, just some retired dude...
batteries good in this new mouse?
put in top brand batteries.
some that come with a mouse are (bottom barrel cheap batteries or are really old and bad from long time on a shelf)
then make sure the DEVICE manager shows the mouse as present.
steps, (generic) (your mousemaker.com will have better advice)
1: be connected to the internet
is first, (after good batteries)
2: then plug in the mouse & USB dongal,
3: here w7 DINGDONG! sound, and then see it try to do PnP
windows, will attempt to find the correct driver for it on the internet.
and if lucky, ( what mouse did you buy?) the W7 finds it and loads this special driver, be aware there are vast makers of mice.
on mine took like 5min to load a BluTooth driver too,
IF this fails. go to CP, control panel
then click device manager.
then see all devices on your system.
look for bad devices or missing.
red. or yellow is missing <marks there.
so. see this, if you see ANY errors here, fix them all first.
right click any and then pick "update driver software"
make sure no USB errors either. this mouse may take 3 working drivers to work (usb-bluetooth-mouse)!! non trivial that...
also if the NEW mouse came with? a CD for drivers? ,use that.