About the scheduled tasks etc. I don't have those, I have also checked for malware and I have had that problem on 2 antiviruses( NOD32 and AVG). About the conflicting applications, I checked and there arent so many apps on launch(only the drivers+antivirus).
Also the network driver is the newest, according the driver scanning tool at the HP site.
The problem isn't exactly the connection speed, more that it some times it doesn't even connect(I get a yellow exclamation mark near the internet icon) until I restart the modem.