TTFB always relates first to LAMP stack tuning, next code like CMS theme + plugins or in your case, what appears to be custom code.
https://www.webpagetest.org/result/160726_A4_1DT3 suggests the likely problem is your LAMP stack or the code generating your home page HTML component.
Look at item #1 + #2.
Item #1 - The HTML component appears to be dynamically generated + is taking 105 seconds to generate + push down the connection to the visitor (browser, WPT, etc).
Congrats on having the 2nd slowest TTFB I've ever seen.
The slowest was a Hosting client I took on years ago who clocked in at 120 secs TTFB.
Item #2 - A small .css file takes 227ms to deliver. A bit slow for a .css file + still way better than 105 seconds.
My guess is your system is resource starved.
Likely best you hire a Server Savant to ssh into your system + check…
CPU utilization (likely okay)
Memory utilization + swap history (likely problem). If your system is swapping, it’s anyone’s guess how long it will take to generate your initial HTML + push it down the pipe.
Do an entire LAMP stack audit, tuning Apache (look for error.log messages about thread exhaustion) + MariaDB (replace MySQL with MariaDB, if MySQL is running), PHP (ensure opcache is on + has sufficient key/pool memory).
After your first audit, run mysqltuner + mysql-tuning-primer daily, till suggested tuning messages all disappear.
LAMP stack basic tuning - areas of focus.
Ensure your disk mount options are sensible. Having reltime on is okay + I prefer noatime,nodiratime to disable access time recording + provide documentation clarity, if someone looks at /etc/fstab to check on mount options.
Ensure your database layer has bin logging disabled (unless you really are running replication).
Ensure your database is using the InnoDB storage engine, rather than MyISAM, so all your tuning can focus on one storage engine, rather than two.
Install XDebug + enable xdebug.scream + log everything to a log file + review to see if PHP is throwing errors during initial HTML generation.
If you get stumped, Skype me, with an Add Contact message referencing your site, + we can discuss your site.