lol, I have a 15" that does that. tony_j15 can attest to this: It would flicker, have "brightening attacks" as you said, and act the same as yours. The way I "fixed" it was to whack it a couple times on the top of the monitor case, and then that would normally stabilize the picture/brightness until I hit it again, or turned it off. Pretty simple really: Whack on, Whack off...
Considering that you could buy a used, but in new condition 19" monitor for around $100 from
http://www.azatek.com and
http://www.merkortech.com it would probably be more expensive to repair the old monitor. YMMV, but normally in the tech world replace > repair.
I've dealt with both companies, and have had great purchases from both.
HTH,
David