Invisible enemy NPCs in SWTOR?

I recently started playing Star Wars: The Old Republic Online. Everything went fine on the starting planet, but once I hit my first off-world mission/flashpoint/what-have-you, I hit serious graphic trouble. Namely, I suddenly ran into enemy NPCs that I couldn't see. And I don't mean they were cloaked: I mean they were totally bodiless. If they had weapons I could see those, floating in the air and held by no one. Half the time I can't even target them, because I can't detect any bodies to target! AOE attacks will hurt them, and about half the time an AOE will cause me to target the NPCs once I've begun to hurt them, but most of the time unless they are accompanied by other, visible enemies that I can target first (which usually allows me to switch targets to the invisible ones using the keyboard controls), I just have to sit there and take damage until someone else kills these invisible jerks.

The problem seems to be linked to what kind of enemy it is, although I can't list all of the ones I've had trouble with, because they don't show up and neither do their names or identities. I can't even loot the corpses unless they're carrying a weapon; then I can click on the weapon and it will allow me to loot, but there's no body to click on even though the "loot indicator" lights up.

Some NPCs that are always invisible:

• Most of the droids on the Black Talon
• Vine Cats
• HK-droids
• Guild Lifter Droids
• Any "boss" droid (in those cases I can see forceshields etc, but not the bodies)

Additionally, some background elements do not render properly, but instead appear as round green cones. Mostly, numerous plants and some security chests.

I have updated all of my graphics, etc., and the computer I'm using is only a few weeks old anyway. It's an Inspiron 5748 with Windows 7, 64-bit, with i7 core. This happens on missions, in Heroic Areas, in Flashpoints, and just walking around the world at random. It affects both of my characters, a bounty hunter and a Jedi Sentinel, equally. They are currently level 12 and level 14, respectively, but have been having this problem since they were both level ten and left their starting worlds. My companions can target the invisible enemies, and so can any other players in the area. No one I've asked has experienced anything like this problem. I've tried playing the game in different graphics settings, but no matter how low or high I set my graphics, the exact same thing happens. This isn't just dangerous for my characters' health; it directly affects my ability to complete missions.

Any help, suggestions, or solutions would be great, thank you!