I am no expert, but I will try.
There could be a problem with your mods, either there not the right version or something along those lines.
I know that the 7 Deadly Sins Mod for Entrenchment is in Alpha testing, so there could be a problem there.
Let's go through somethings
[ ] Is the Mod the right version? They need to be compatible with version 1.051 entrenchment. For many mods you have to wait till they update it to work with your current version. If it isn't the right version, you could try this (https://forums.sinsofasolarempire.com/356807) which is Harpo99999's mod updated. It doesn't work with every mod, but it can help.
[ ] What is the Mod? Is it in beta testing? Is it complete? There may be bugs in the Mod's itself. Not all mod's work. From what I know, 2 things can happen with a bad MOD.
1) It will result in a mini-dump, crashing your game.
2) It will be stuck in a "loop", where there is a glitch and get stuck doing the same thing over and over.
[ ] Is there something wrong with you computer? Bad Graphics card etc...
[ ]Is there something wrong with your Game? Is there a glitch that you cannot find?
I am pretty sure something isn't wrong with your hardware, because my computer can run Sins of Solar Empire and Mod's with only 960mb of ram, single core 2.00ghz processor and no (besides on board) graphics card...
Hope this was helpful in anyway possible.
IS IT SPOCK? ----> 
(no point really, just really wanted to try this face thingy)
