I understand that the change is for the better, but as I miss the day when engineering in a start-up meant C/C++ hacking in a UNIX environment, as evidenced by Richard Stevens' books on Max's shelf:
Even though you no longer _need_ to be a C hacker to build a web application (and that's generally a good thing, as anyone at Paypal who still deals with the legacy C++ code, or anyone at Amazon who remembers OBIDOS can tell you), you should still work your way through Advanced Programming in UNIX Environment, and UNIX Network Programming: you won't regret it a bit.
If you want to learn low-level programming but aren't really enticed by networking / operating system hacking, I'd recommend writing a software rasterizer. It's a fun project, and it's satisfying at a visceral level to see your creation come to life.
And it will make you a better programmer for the rest of your life. If nothing else, you'll come away with a much more solid understanding of memory, CPU caching, etc.
Here's my (terrible) software rasterizer: http://dl.dropbox.com/u/315/programming/demos/viewer.zip (Windows only, sorry. But there's no reason why it has to be. All you need is the ability to make a pixel change color, and you can therefore write a software rasterizer.)
http://levchin.com/images/PayPal/1840-yellow.JPG
Even though you no longer _need_ to be a C hacker to build a web application (and that's generally a good thing, as anyone at Paypal who still deals with the legacy C++ code, or anyone at Amazon who remembers OBIDOS can tell you), you should still work your way through Advanced Programming in UNIX Environment, and UNIX Network Programming: you won't regret it a bit.