From my point of view your "inxi -Fxz" report reveals no obvious problem or misconfiguration. Looks perfectly normal to me. But I do not pretend to be able to detect any potentially problematic hardware component just by spotting its name.
The .xsession-errors file seems to document a problem affecting the sound system, not necessarily a hardware problem, might as well be a software problem.
I wonder a bit whether Mint 17 has really been installed completely or whether some software packages might be missing. - Just a vague impression, not a fact.
As so far no-one seems to have had any idea what the root cause might be, I would like to have a closer look at the syslog file (/var/log/syslog). It is a pure text file. You may open it with any text editor or with the system log viewer (gnome-system-log).
The interesting timespan will be the period when the LM17 starts up.
One of the first log entries which will be created during every startup is when the logging daemon itself has been started. Will look very similar to this line
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Jun 30 12:50:59 machinename rsyslogd: [origin software="rsyslogd" swVersion="5.8.6" x-pid="517" x-info="http://www.rsyslog.com"] start
The 2 or 3 minutes following this line will be of interst, because they ought to hold some (error) messages.
Please, copy the syslog lines into your clipboard and paste them into your next reply.
(If you cannot do so on the malfunctioning machine, then copy the syslof file to a USB pendrive and do the copy and pastee from the machine which you use for visiting this forum.)
Have you tried booting the failing machine from the LM17 live system (which you used when installing as well)? Did Cinnamon crash on the live system as well?