Get a price quote for repairs before considering it. Be aware, that you might be taking the monitor for repairs often after the first one. You would do MUCH better by getting a new (and good branded) monitor. It's also less hassle, and you won't have to wait however long they take to repair the monitor.
You CAN purchase a BRAND NEW Sony or ViewSonic 19" screen for about $300 (from Best Buy of all places).
http://www.bestbuy.com/detail.asp?e=11089110&m=488&cat=497&scat=500
If you really have your heart set on getting your old monitor repaired, find out from the manufacturer if there are any authorized repair centers in your area. They are authorized for a reason (they meet the requirements of the monitor maker to make quality repairs and not screw the customer).
With the 19" ViewSonic being under $300 (after the rebate, $280), you need to decide how much your old monitor is worth to you. You could take it for repairs this month, and have a different part blow next month (if DOES happen), then you will have to shell out more money to get it repaired again. A simple tv repair typically runs over $100. When you are talking about a $600+ tv set, then it is worth it, not when you are talking about a monitor you can replace for under $300.
Hey alex... you want to suck my what??? Sorry, only women are allowed there.