Don't worry about the led on pin 13, it just sits there but doesn't block anything.
You can still use the pin as a normal IO pin.
You didn't mention whether your 30 inputs are digital or analog, so let's have a look at digital input first.
I have never used the MCP23017 mentioned by Martynas, but the linked article looks very interesting and I'll definitely order one of these amazing chips!
Another option might be using 8 bit PISO (parallel in - serial out shift registers, such as the 74HC165. Consider this as the complement to the 75HC595 for output. These shift registers are dirt cheap (around 0.3 €), are available as DIP (important for breadboarding) and can be run via SPI.
it's fast to read in 8 digital lines into a byte (why would one want to use more than a bit for the state of a digital input?)
the shift registers can be daisychained, subsequent calls of ShiftIn allows to read all (digital) input states into a corresponding data structure (array of bytes, etc.) using just three pins on your Arduino.