I encountered a similar problem on a client’s ancient XP system recently (yes, I know, I did recommend a newer system and OS). It wouldn’t allow downloads (straight up wouldn't even allow those pages to load at all), but it would allow installations. So I whipped out my CD with MSE and MBAM installers and cleared it right up (it was really bad – 404 error on every solitary page that had a download on it. Pages without downloads loaded just fine. Weirdest case I’ve seen yet).
If you don’t have access to another system to get those installers with, use a friend’s (even a neighbor’s) or the public library system to get the installers on a CD/USB stick.
Now, if its circumventing BOTH downloads AND installations... well, have you tried to use
System Restore? Try to roll it back to the farthest restore point you have (tick “show more restore points"). If it’s nothing really nasty, that should clear it out. If, however, you don’t have a restore point predating the issue it won’t do anything and I’m unsure of what you could do other than a full factory restore/clean install, unfortunately. I mean, if it’s not allowing downloads AND installations. That’s very tricky.
Well anyhow, after you get it sorted, I would have to strongly recommend the pair of MBAM and MSE (they do not conflict). Additionally, AdBlock Plus and NOT using the IE browser (poorest security), go for Chrome or Firefox. I haven’t had malware in more than two years with that combination and practicing safe browsing habits (I did go Pro on MBAM. It’s absolutely worth the nominal, one-time fee for the live scanner. Also actively scans for malicious sites and rootkits).
