Mac won't boot into recovery; might be related to Time Machine
I recently purchased a new Mac with El Capitan. Last night I finished a Time Machine backup to my older Mac (also El Capitan) and installed the Time Machine backup on the new Mac. When it was done installing, it ceased to function - I just hit a blue screen. After an hour or so I rebooted and it has never progressed past the Apple symbol and the spinning wheel. I tried to reboot into Recovery Mode to try a re-install but it won't let me. I then went into Safe Mode with the reports turned on and it never completed booting up, it kept having the same error pop up - "tried to access a compressed file or unregistered type 7" or "8" over and again.
I'm at a loss. Is there any way I can boot into Recovery Mode, or otherwise get this machine running again?
Thanks for your help.