What firmware is your phone running? Just trying to root shouldn't brick it, even if you're running one of the OTAs that patched the exploit.
Did you try holding the power button until it turns off? It sounds like it's still on if it makes the connecting sound when you plug it in. Try holding the power button down until it does a hard shutdown, then see if you can get into the bootloader manually (hold down both volume rocker buttons and then push and hold the power button also).
Device: Motorola Droid RAZR HD XT926 | Bootloader Unlocked & Rooted | Recovery: TWRP 126.96.36.199 | ROM: CyanogenMod 10.2 nightlies