Do it the easy way. Sort that list by process name (click the process tab) and print it. Make a new user on your computer, log in and sort the procees list, compare the two.
I use Adaware and I've heard good things about Spybot. Both are free and work great.
Do you have Zonealarm? If not, download the free version. It will ask if you want something to access the internet, so if you recognize the program that is asking to go out, let it. If not, tell it NO and see if everything still works.
Once you know what programs you want to access the internet, click the little box that says "Always allow this program access" or something like that, and it won't ask again for that program.
Close all other programs on your computer, go back into task manager. Any that are started by you are suspect, like that hphmr08 or whatever the hell it is???