iTunes Match or Apple Music would provide a way that allows media added to your computer's library to be accessed over wi-fi, or even mobile data if you have the bandwidth. The data comes directly from Apple's servers once your library has been matched.
On the other hand you might want to focus first on getting your data backed up before the computer fails completely. 😮
You should also backup the device to iCloud if it doesn't already do so.
As given syncing is generally from library to device, though media purchases may flow in the other direction. Should your computer fail and you find you want to start using your device with a new computer see Recover your iTunes library from your iPod or iOS device.
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