What version of roms do you have, there was a problem with one of the revisions with the game blacking out like that.
Read the service buletins on sterns sight for this game and get the latest roms in there if you don't have them already.

Version 5.01 is the highest eprom version for Jurassic Park according to ipdb.org

Yes, it is just as simple as replacing the EPROM with a new one, just be sure and observe correct polarity when installing the new EPROM. Do not go by the label/decal as they can be on backwards or forwards.

You can purchase from:
http://www.actionpinball.com/roms.htm#pinball
or one ebay from ROMPINGIRL
both are just a suggestion to get you started.

Lots of places have pinball eproms. If you had an eprom programmer you could download the code and do it yourself. Not recommended for the novice but it is good experience and you have to learn it somewhere. Then pinball repair will be in your blood.

Here is some reference material for Jurassic Park for you:
http://www.ipdb.org/search.pl?any=jurassic+park&search=Search+Database&searchtype=quick#1343

Never apologize for being new... I love reading threads like these because it helps me better understand problems that I might have in the future. Good luck with solving the problem!

Ipdb is confusing sometimes with the rom versions.

The latest version for the CPU is 5.13 and for the display is 5.10

Upgrading to those versions will correct your issue.