Sorry to keep posting but I finally figured this whole thing out. I wanted to share because maybe it will help someone. I run 2 dolphin pro 7.2.1 installs. We will call them Site 1 and Site 2. Both sites were not able to embed YouTube videos after updating to 7.2+. Both sites are running PHP 5.5. The 5.4 environment reacts the same (I tried).
Site 1: Showed "file failed upload" error.
Site 2: Showed nothing. File simply would not upload. After clicking the button nothing happens.
Site 1: Updated my cron path to php 5.5 and it started working.
Site 2: Updated cron path to php 5.5 and it changed nothing. Embed continued to do nothing.
I then remembered that I had this issue a long time ago with "mod security" blocking video embeds. For those of you who run mod security on your server this might be your problem also. I had already applied a fix for this to Site 1 .htaccess file in the past so this is why it was working already after updating my cron and why Site 2 was not.
Before you get too deep into fixing this, you can first see if mod security is even the problem. If you run mod security then you will most likely have an option in your hosting Cpanel that allows you to turn mod security on and off. Turn it off for you domain and see if the video embed starts working again. If it starts working again then without a doubt a couple mod security rules are your problem. If you do not have options to control your mod security options then contact your host and see if mod security is enabled for your domain.
Option 1: You can just leave mod security off. This option is acceptable but I prefer mod security any day if possible.
Option 2: To continue running mod security leave it turned on and add this code to the very top of your .htaccess file in the root of your site. It must be at the very top of everything to work on most servers.
<IfModule mod_security2.c>
SecRuleRemoveById 340162
</IfModule>
<IfModule mod_security2.c>
SecRuleRemoveById 340163
</IfModule>
Save the .htaccess file and clear your cache in the admin panel. Now make sure that mod security is turned on and try your video embed again.