Spyware collects data which it sends to commercial organisations - these people collect it all up from millions of users around the world - tabulate it and then sell it on to marketing organisations. It spys on your web browsing habits and cares nothing about your e-mail traffic.
There will very probably be spyware in your computer unless you have taken steps to remove it but the spyware will not prevent you from logging on - if it's a password issue then ask the person who set up the password in the first place.
Your question is confusing - is it an e-mail problem or a password problem or an internet connectivity problem? You seem to claim all three which is doubtful and then talk of spyware which is not appropriate.
You fail to mention the OS - the make & model of the machine - your method of connection - when it last worked - your ISP - your e-mail client.