Computers with physically damaged all USB ports are rare - however they still exist in the real world. The below guide should help you choose proper cables, that could help you with such computer.
But let's start from the simplest case.
Before trying to open your computer, check very carefully, if USB ports are enabled in BIOS or UEFI configuration.
Most computer vendors allow to disable or restricts external USB ports for security reasons. Some of them, eg. newer models of Sony Vaio laptops, or many models of HP ProLiant servers, have 2 separate switches in BIOS configuration: to enable USB ports and to enable booting from USB ports.
If BIOS reconfiguration wasn't enough, it's time to open the computer case.
First of all, you should have a set of basic computer screwdrivers. Nothing special, unless you also want to deal with Apple hardware - just basic ones. For example, author of these words uses a very similar Chinese set, bought in Poland for just $2:
What you're looking for, are internal USB goldpin connectors. Because of 2 main reasons:
Now, there are 6 common types of goldpin USB motherboard connectors:
In "proper" connectors:
Unfortunately, some cheap motherboards use 5/10/20-pin connectors instead (with 2 unconnected pins).
From the electric perspective, USB 3.0 is much more complicated than USB 2.0. It is possible, that some signal lines from USB 3.0 are damaged, but port is still able to work in USB 2.0 mode.
In such case, we also recommend this female 19-pin to male 9-pin cable.
If internal USB ports also don't work, you have to disconnect internal drive(s) and connect them to another computer:
Unfortunately, moving the drive to another computer won't work with TPM chip (if that drive is encrypted using Bitlocker).