You're starting out with a bad quality source. Your internal soundcard is (as the name implies) internal, which means all the data passing nearby (HDD, CPU, USB traffic, Wi-Fi) as well as power supply noise gets into your recording. That's where the static comes from. You can only do so much in post-production, and as you've learnt first-hand, it is time- and labour-intensive. Which is why you should think of it as a last resort. Repairing audio to a decent quality costs at best lots of time, at worst lots of money, too. The tools are expensive because they're mostly used in movie editing and those people will pay every price to meet the deadline.
The industry-standard tool for that is iZotope RX, priced from $129 all the way up to $1199 for the full-featured version. For a comparison chart, look here. The $129 version used to be called iZotope RX Plug-In Pack, but now they offer the standalone editor as well as plug-ins which you can use in Audacity or any audio editor you'd like. Here are some highlights of what you get:
- Clip gain (draw a curve to fade in/out or minimize volume changes)
The higher-priced versions include a variety of additional tools like De-plosive, De-reverb, Ambience Match (which lets you record at home and add the background noise of an outdoor recording, handy for movies) and Leveler (automatic tool for getting consistent volume). That said, the price is much higher for these tools, as these are geared towards movie production.
Another alternative is Waves plugins, which are another industry-standard tools. These are a bit more costly, though. There's a full Restoration bundle (de-noise, de-hum, de-click, de-crackle), but it's $749, currently on sale at $399.
From my experience, iZotope is the standard, and for good reason. It works better than Waves every time I try it. That said, there's one affordable ($149 regular, on sale $49) and really easy-to-use plug-in from Waves that I can honestly recommend - NS1 Noise Supressor. It does noise reduction, it does it really well, and it couldn't be easier to use:
This might be your rescue. However, I'd really recommend you to grow up and use proper tools for the job - now's the time to get yourself an USB microphone. You'll get an infinitely better result starting with a quality sound source, and you'll save lots of time. Samson C01U is $35 for the old version, you can get the new one with headphone output (for hearing yourself while you talk without delay) for $72. Behringer C-1U is $48 and this is what I've started with. Get the one that's the cheapest in your local stores, or have a look at used ones. There are tons of rappers around who realized they're not that good after a week or two and now sell them for really cheap.
PS: The reason you can hear noise on headphones is because listening through your laptop speakers gives you absolutely no clue about the sound your playing, especially in terms of quality and noise.
PS2: Sorry for the lengthy response, but hope you find it useful!