A 4 year old computer is likely to have around 4 GB ram. The age isn't the problem, your internet bandwidth isn't the problem either.
You can probably greatly improve your download speed by replacing your HDD for SSD (or keeping the HDD as a spare), adding more memory (16 GB or more if your PC supports is), and increasing your dbcache setting in Bitcoin Core. Your entire computer experience will improve from using an SSD instead of HDD too.
Or just use Electrum, it's much less demanding than Bitcoin Core.