I have a Samsung HL-R5667W that is about 3 1/2 years old. The screen is dark except for occasional flickers of light. The lamp appears to be giving off light when I look in the back. I replaced the bulb about 1 year ago. When I plug in the cord, I hear the normal beeping as it warms up and I see "lamp" illuminated within the on/off button, then it goes dark and it stays dark. When I press the on/off button, nothing happens and I can still hear the fan running in the rear. I turn off the TV by unplugging the cord.

most likely optical engine issue----bad light engine.

how extended is that warranty, and what does it cover? Sounds to me like a classic video controller board about to fail.

You TV is a DLP and only has one lamp.
Check this link to find the lamp for your TV.

If you get on screen display with no picture and no sound, I suspect you have a failed digital board. Go to http://www.samsungparts.com you will need the COMPLETE model number IE: HLR5667W or HLR5667WAX to figure out which board you have and then you can order it from there as well. The board they sell has NO metal shielding around it so when you order the board you pull out your old one once you receive the new one and swap the metal shieding from old to new. ..Please take a few minutes to rate my answer...Thanks

It looks like DLP chip is failing. It is installed on DMD board that in turn belongs to optical engine. Issue should get progressively worse. If you look at screen up close - you see that "tumbprint" consist of little small dark-gray squares, some of them flickering.
Cheapest solution - to replace DLP chip. instead of replacing whole optical engine.
This repair have to be confirmed (by running test patterns in service mode first) and done by professional.
Repair could cost aroung $400.
During procedure I would recommend to turn ceiling fans and other air blowing devices off. Single little dust speckle landing on the chip surface will ruing all effort and same amount of labor have to be applied yet again just to get rid of it (been there, done it).
Good luck.
Russ.

Purple spots means Bad Light Engine Part number is BP96-00822J Encompass Parts Has them for
$950.00 - $350.00 core price Part $600.00
1-800-638-3328 Lamp# BP96-01073A

Ballast Board# BP47-00027A

If you have never replaced the lamp it is most likely to be the problem.Most lamps last 2-3 years under normal use.

the problem will be the board

You may have a colorwheel going bad. The bearings start going out and this is an indication of the failure. The colorwheel is located in the light engin e therefore you may want to get a qualified tech to look at it

I just responded to your other post check the connection between the lamp and ballast at both ends. Also did you get the same exact lamp as your old lamp, as Samsung has two different arc gaps and they wont work if you get the other type even though they look the same physically.