When you say running in slow motion, does that mean the character appears to actually be running slow while everything else is moving normally? Or does the whole game appear to be slow?
Also, how long does it continue? For a while, till you restart eq or the computer, or just some random amount of time?
Some things you can do...and if you do not understand what these are or know how to do them, then grab your computer nerd friend or family member (everybody knows one).
Delete temp files on the computer and defrag the hard drive.
Run task manager before running eq and shut down un-necessary things; clean up the startup programs (lots of "freeware" and "shareware" that people install add things to the startup programs).
Don't run a browser while you are running eq (like the item above, lots of things like to install add-ons to our browsers, if we are not careful, and they can slow things down).
Unplug everything, crack open the computer case, take it outside and blow it out with compressed air (not on a rainy day, do not tip the compressed air too far from level as it is stored as a liquid and will "burn" you or damage equipment). Pay special attention to the cpu heatsink and fan, video card heatsink and fan (if the card is not integrated), the ram, and the power supply fan(s). Dust is a great insulator and heat is the enemy; many computers will slow down the processor, or shut down, if too much heat builds up.
How much ram do you have? If you have windows xp you want to have at least 1 gig of ram, 2 or 3 is better. For vista or windows 7, 2 would be a minimum and 4 or more would be better.
Video memory is a concern also; the the video card is built into the motherboard then try reserving more memory for it in the bios. Also, if it is built in, consider getting a new video card with at least 512megs of ram, but again more is better and I would suggest 1gig or more.
How full is the hard drive? If you have 500 gigs of hd space and less than 20 gigs free it's time to clean it up or add another hd for all your videos, pictures, and music.
That's all I got at the moment