Dell 2001FP monitor colour vertical stripes flickers on right after few minutes

Most likely, this is failing "inverter."
The backlight of the monitor (that makes the image visible) is controller by a special chunk of electronics called an inverter. They tend to fail over time. The symptom is that the backlight either never comes on, flickers, or shuts off after a short period of time.
It is a moderately advanced repair job to change out the inverter, but you can usually get the part on eBay. Search for the exact monitor model number and "inverter".
The 2001FP has six lamps and the inverter is fairly expensive. You might be better off putting that money towards a newer monitor.

You have failing T-CON board, new LCD panel is needed since the T-CON is part of the LCD panel assembly.

Failed TV and Monitors: http://s807.photobucket.com/home/budm/allalbums

http://en.wikipedia.org/wiki/Capacitor_plague

Basic LCD monitor troubleshooting guide:

http://www.fixya.com/support/r6150077-basic_lcd_monitors_troubleshooting

Bad lamps will either does not light up or have pinkish color. More likely to be T-CON board, check out the connection between the T-CON board and the Logic board. If the lines are vertical lines from the top of the screen to the botom of the screen, then that will be bad T-CON board and not much you can do, new LCD panel will be needed.
http://s807.photobucket.com/home/budm/allalbums
http://en.wikipedia.org/wiki/Capacitor_plague

It sounds like it is either the video cable or the video causing this if it is happening on more than one monitor. I would replace the video cable first and test. If it is still doing it you can install the video card in a second computer to test it. Or just replace it.

I'm having the same problem... there's also going to be about 5 years of dust sitting in there, so I hoping it might just be a failure of convective cooling. My first attempt to remove the bezel was unsuccessful, so I wasn't able to go in and look for any swollen capacitors or such. I have blown canned air in the sides, and it's actually doing a little better right now. Probably won't last... having a rather warm summer.

http://www.lcdrepair.us/2001fp-logic.html

The board that you may need.

does not help. keep dvi connector (white one) on computer and in the back of monitor.
and surely it will not take away those vertical stripes.
those vert stripes... hmm... your monitor might have a problem which you can't fix by your own.

Full instructions from DELL at:

http://support.dell.com/support/topics/global.aspx/support/dsn/en/document?c=us&docid=FC55E86F0611BEE3E030030ABD620A8C&l=en&s=gen

Please rate this response thanks.

Sounds to me that you have a bad connection/wire to the CCFL bulb on that side of the display. Should be an easy fix, do it your selfer thing.