Usually there are no other alternatives than to go for broadband internet connection with reliable speeds. However unusually one can use RDP (Remote Desktop Protocol) which can give you speeds of over 64 Mbps. Although it does require technical skills to operate it which is the drawback of this tactic.
Internet speed does depend on your processor to an extent. Relieve your processor of unwanted program running so that the downloading does not get hampered. Try using minimal programs while accessing internet and downloading data. You can also use faster browsers like Google chrome to access internet faster as it requires low processing speeds.
