Dot Matrix IC message board
Why do you need to use a ROM or EPROM/EEPROM? How are you planning on using that to drive these LEDs?

What you're trying to do is easy to accomplish with any microcontroller. You'll need to multiplex the LEDs (so you don't have to drive each individually) and connect at least one side of the LEDs (rows or columns) to a driver like the ULN2803. There is tons of information on the web about doing this.

A google search for "led matrix microcontroller" turns up:
http://www.create.ucsb.edu/200C/2008_Students/MAT-200C_2008_Files/matt_stabile/MAT200CStabile.pdf

http://www.best-microcontroller-projects.com/led-dot-matrix-display.html

http://www.instructables.com/id/48x8-SCROLLING-MATRIX-LED-DISPLAY-USING-ARDUINO-CO/