There are different reasons why this could happen. First I would try the following:
Add swtor.exe and launcher.exe to your Anti-Virus / Firewall exceptions / ignore / safe list or whatever it's called for them.
Once that is done try to run the game again. If it's still crashing run a repair:
Non-Streaming launcher - Log into the launcher but don't click Play. Check for small letters "ST" in the bottom left corner. If this is NOT present, With the new launcher after login , select the username pull down on the top right and select settings, then press repair.
Streaming launcher - If the letters "ST" is present, close the launcher, right mouse click on the game shortcut, select open file location and delete the BitRaider folder. Then start the launcher.
If that is still not working you can also switch to the non-streaming version of the launcher. The default installation is the streaming version which uses bitraider, I've heard of bitraider causing issues for some so removing it may help. Here are the steps below:
NOTE this is a complete download of the game again
right mouse click on game shortcut and select open file location
open the launcher.settings file in notepad and locate the below line and edit to the below
, "PatchingMode": "{ \"swtor\": \"SSN\" }"
, "bitraider_disable": true
SAVE the changes.
Delete the BitRaider, Movie and Asset folders then start the launcher.
