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I have dealt with this problem with Lenovo computers before.
Try holding down Fn key on your keyboard.
Then while holding it down, press the F9 key - but only ONCE.
Then let go of both keys.
Then wait a half a minute! this may be important.
Then try the trackpad again, and the mouse. (If you disable one, you may disable the other.)
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Alt keys can work. Alt-Tab switches between windows/programs.
Alt-F4 closes exits the currently open and selected window/program.
That plus the arrow keys and the space bar (to highlight/select something ?) and the Enter key (to 'double-click' something/icon/program) will probably see you through a lot, with some patience.
But: what is the old computer, an Acer?
Try Fn-F9, once. See if it helps. It's good on more than one maker's PCs.
Let me know how it goes, etc.