Your friend is very likely correct; all you needed to do was to go to the "Performance" menu option (the one that W3TC installs) and go to the "Minify" sub-option. You can enable or disable it there, and select the level of "aggressivity" you wish to use Minify for.
In some hosts, checking "Rewrite URL structure" will fix the problem you've been having. In others, you might need to disable Minify completely. I have had similar CSS issues in the past, but the problem was almost always on the host configuration — I use several hosting providers. When I have full access (e.g. root account) on the host, I can obviously tailor it to suit W3TC best, of course, but on shared hosting accounts I'm limited to what the provider gives me, and so I have to tweak W3TC appropriately.
Please note that W3TC is not the culprit :) It's a fantastic plugin but ever so hard to configure properly. Unlike most WP plugins, which will work pretty much on all hosting providers out there, W3TC, due to the clever tricks it uses, has to work in tandem with the webserver software, and will try to make the best of what it can do — but sometimes needs human help to tweak settings. I can tell you that a server specifically tailored to work with W3TC can give your WordPress install such an increase of performance that it becomes uncanny (I've seen static sites that are slower to load!).
If your hosting provider has such an odd configuration that W3TC can help little to improve performance, you have two choices. The first is to use a different caching plugin (WP Super Cache remains still a good choice, and it's easier to configure). The second, if you have full control over your DNS, is to use an external CDN — you can use CloudFlare, which is free, and fully integrated with W3TC. I have a few blogs on shared hosting (where performance depends so much on what the other users are doing...) with CloudFlare on top of everything — I get some 50-55% bandwidth savings that way, which is not bad for a free service. No, it doesn't mean that your site will suddenly become twice as fast: it means that only half of the requests will go through to your shared hosting provider, and those requests will be superfast. Static images, CSS, JS, and embedded elements can thus be immediately served from CloudFlare and will never reach your WordPress installation. And W3TC will prepare that all for you automatically.
It's worth giving it a try, but, of course, you will only see serious improvements on very busy websites.