It is very complicated to connect to the internet! Think about it:
Your computer might have multiple ways of connecting -- WLAN, Bluetooth, Ethernet, etc. Each of those has its own settings, which you need to set. You're lucky that there's already standards and drivers for these... using these could be a lot harder than it already is right now.
IP addresses can be IPv4 or IPv6, and you need to be able to handle both.
There may or may not be proxies configured for the system.
You have to support FTP, HTTP, or some other protocol.
You might need to use dial-up, so you have to specify a phone book with passwords and phone numbers, if you're not already connected. Ditto with WLAN usernames/passwords.
You might need to work with cookies.
The system might cache some data, so do you want to use the cache or not?
and the list goes on and on.
So the fact that it's easy to do these with Python necessarily means that a lot of these are hidden from you (or difficult to set), so you trade simplicity for power. The C library is the opposite: it has all the power you need (you can easily perform system calls), but doesn't have any defaults (or, in fact, any features for connecting to the internet).
Instead of thinking of C as being tedious, think of it as being powerful. But in any case, don't try to connect to the internet with it -- that's a pretty darn hard thing to do. Instead, start learning how to use the library for more basic tasks (e.g. file I/O), learn about how pointers and arrays really work, and when you learn all those, then try tackling big projects. You'll appreciate Python more that way too. :)
I personally suggest that, if you have free time, learn C# first instead. As soon as you get comfortable with it, start learning about the
unsafe keyword and how to use pointers and do marshaling in C#. You'll still have a really big library to work with, like with Python, but you'll be able to do a lot of things that you can do in C. Then transition into calling system API's manually (like InternetOpen), and learn how to get those to work. You'll still have a lot of flexibility but you'll get a great introduction to lower-level concepts. After you've done these, then start learning C -- then you'll find it to be a piece of cake, and you'll see (C? get it?) the advantages and disadvantages of high-level and low-level languages, and you'll be able to find the one that suits your needs.
That said, I think A Crash Course in C might be useful as a starting point to jump into the