Before you reinstall it, there are a few steps which can REALLY help that are easy to try and report back on.

Step 1 - Google AdwCleaner, download and run it. It's a tiny one-shot malware/nastybugs cleaner that in my experience is not only much more effective than your typical cleaners, but also doesn't take 23 years to run.

after that :

Step 2 - Download CCleaner and run it. Before anything else, click on the options button and then 'monitoring', and uncheck the boxes. The last thing you want is more stuff running in the background of a slow machine. Good. Okay now click 'tools' and then 'startup'. Disable EVERYTHING, unless you're super 2000% sure he wants it running on every boot. Most stuff that you can disable here can be run manually by opening the desired application anyway. And right under the 'startup' section, you'll see 'Browser Plugins'. Handy! Now this is trickier, but disable things which are obviously not needed for standard browsing. All that done? Good, now run 'cleaner' from the main page and take out the trash. (optional : go down to the system restore tab on the page where you select startup or browser plugins, and clear out all but the most recent restore points. - this makes defragging easier).

Step 3 - Defraggler. This is also from piriform.com, and will do a better/faster job than the built-in W7 defrag. This may take a while, so I recommend disabling the power management 'go to sleep' timeout, and letting it run overnight. Sometimes you have to run it twice to get the best effects.

Boom! That should at least help the poor thing to run as good as it can. It also is worth looking at http://midori-browser.org/ to see how Midori fares on that system. Chrome is generally terrible on weak hardware unless you never use tabs, as Chrome will generate an entirely new Chrome.exe process for every tab.

Anyway good luck. These three tips are pretty much gold for any Windows PC, though if you have an SSD you can skip the defrag.

Firefox doesn't currently create a new process for each tab, but that supposed to change 'some time' in the future. So you can evade the process problem for now by using Firefox, but it's not a long-term solution if you want to update your browser (and you should, always, for security purposes). That said, I've had Firefox running on some weaker computers and it seems to be doing just fine, so maybe it'll work anyway. I'm having some occassional freezes and there's a gigantic memory leak that happens on Twitch, but overall it's been fine for me.

If you need a really lightweight solution, Midori ought to be one. There's also some browsers based on Firefox that should be more lightweight than Firefox itself.

For performance, I suggest installing an adblocker (preferably uBlock Origin (which is different from just uBlock), because it's supposedly pretty lightweight compared to e.g. Adblock Plus) for whatever browser you end up choosing. I think it's supposed to help because your browser won't have to load ads anymore. Also make Flash etc. click-to-play, it's helped me a lot and my PC is relatively powerful so the effect should be noticeable.