How to exit Recovery Mode on jailbroken iPhone
Based on the fact that you're stuck at the Apple logo, it actually sounds like you're stuck at boot-up instead of being in recovery mode! It's likely that a tweak you installed caused it to enter what is often called a "boot-loop" when you restarted it.

To exit this, try holding the power and home button for ten seconds like you saw in those guides, but this time as it restarts, hold the volume-up button. This enters the Mobile Substrate's safe-mode (thank you Saurik for your foresight!) and should allow you to access Cydia to remove the troublesome tweak. If your volume-up button doesn't work, use your Apple earbuds and use the volume-up on the headset remote.

EDIT:
After digging through the problem more and trying my suggestion, the asker could not boot into safe-mode. Booting into DFU-mode and restoring via iTunes was the only viable course of action to solve their problem.