Ah, thanks for the help! Sorry, I forgot to check this, but I've been e-mailing customer services to try and get some answers...
Fixes I have tried so far:
1) Uninstalling/reinstalling Origin
2) Uninstalling/reinstalling Mass Effect 3
3) Checking for updates for Origin
4) Checking for updates for Mass Effect 3
5) Using Origin's repair function on Mass Effect 3
6) Updating all of my drivers (video, sound card, network adapter)
7) Using a different version of awc.dll (fix from earlier this year) and EACore
8) Copying Mass Effect 3 to desktop, reinstalling, quitting Origin, then copying Mass Effect 3 back to the main folder
9) Running both Origin and Mass Effect 3 as an admin
10) Removing awc.dll, then trying to launch Mass Effect 3
11) Repairing via Origin, then trying to launch Mass Effect 3
12) Moving Mass Effect 3 to desktop, then trying to launch Mass Effect 3
13) Uninstalling Mass Effect 3 from my registry
14) Running Mass Effect 3 without DLC
15) Deleting local save game data
16) Going through Task Manager, disabling every process except Origin, then launching trying to launch Mass Effect 3
17) Trying to launch Mass Effect 3 with Origin in-game disabled
18) Changing my email/password associated with Origin
19) Trying to change core affinity and run ME3 in a dual-core mode
20) Running CCleaner and a registry cleaner
21) Disabling User Access Control
22) Running ME3 from a new user account
23) Running ME3/Origin without being connected to the internet