I had this same problem (iCloud for PC - Windows 7). For me, Photostream stopped syncing properly over a year ago, and after a recent iCloud (PC) update, I couldn't even log into iCloud anymore. It would crash every time during the log in process. I tried everything I could think of (installing, reinstalling, etc.). I had pretty much given up and stopped using iCloud since last Fall. I'm happy to report now that I have fixed it. I know this is an old thread, but I'm leaving this here in case someone else comes across it (which I'm sure they will).
Other people who have had this problem mentioned something about having to reinstall Outlook to fix it. Maybe that would work for some people, but since I don't have Outlook, that wasn't going to work for me. Here's what did work: I disabled the Apple Push program from starting up with my computer.
In case you don't know how to access that, go to your Start menu, and type "msconfig" in the Search box. Once you hit Enter, the System Configuration tool should open up. Click on the Startup tab, and you should be able to see all the programs that startup with your computer. Uncheck Apple Push (along with any other program you want to disable), and hit OK. You will need to restart your computer for the changes to take effect.
What does Apple Push do, and is it safe to disable? Supposedly, it helps your iDevices communicate with iCloud, etc. I can tell you right now that my iPhone communicates with my computer fine (better actually, since it's finally letting me log into iCloud and see my Photostream properly now) with it off. After some internet sleuthing, I've actually found that many people recommend you turn it off to help your computer run faster.
This wasn't something that I was actively looking to do when I found out that it worked. I had pretty much given up on having access to iCloud on my computer. I had another program that I wanted to disable from starting up automatically, so I went into System Config, and it was there that I noticed that Apple Push was even a thing. Anyway, I unchecked it (since I wasn't going to use iCloud anymore anyway), and then restarted my computer. Since iCloud was back on my mind, I decided to try logging in again. I didn't have any expectations when I did, but lo and behold! It actually worked! To top that off, Photostream was syncing again!
Anyway, hope this works for you! Good luck!