Monitor goes to powersave mode in the middle of using computer.. tower does not mouse and keyboard will not start it up again or bring the monitor back from hibernation

The monitor has failed, it is almost always cheaper to replace it than fix it.

Unplug all the Cables from Compaq Presario 5103 CL and leave the Keyboard, mouse and monitor cable pluged in.

Now make sure the power cable of the monitor should be pluged in and the power cable of the tower should be pluged in.

Now to check if the montor is fine just unplug the video cable only which will show no input signal on the screen. If it shows this signal the monitor is fine. Plug back in the video cable.

If the monitor is going to sleep mode it might be possible that the old computer ( Compaq Presario 5103 CL ) is in stand by mode. hit any key on the keyboard and it should come back .

If it is not in the stand by mode then do one thing. Check the same monitor with the new computer. If it is working. Perfect ..!

Do one thing now ..!

Unplug all the cables from your old system and then press the power button for 30 sec and let it go. Now plug the keyboard, mouse and the monitor try again.
If it works Perfect. If not ..!

Then you need to open the tower and check on the processor FAN is it running..? If its not running you will not get the display as the fan is responsible for the display on the screen. Otherwise...!

Check the Tower possibly the Tower is not getting the power.

Try these steps and let me know If it works

looks like there is problem with ur signal cable check that monitor signal cable is tightly fixed or contact ur product support center.

If you've moved your whole PC recently then you might need to make sure that the VGA cord is connected to the correct output on your computer and is screwed on tight. If that doesn't work then try replugging it.

Dell monitors automatically go into power-save mode after a preset amount of time when the computer is inactive. The Dell monitor will go completely black, instead of showing a screensaver. This doesn't mean that your Dell computer has shut down. Instead, this allows your monitor to essentially turn off until it's needed again. You can change how long it is before the Dell monitor goes into power-save mode by changing your display settings.

1. Step 1 Press any key on your keyboard or move your mouse. Either will turn off power-save mode. Alternately, you can press the power button on your Dell computer tower or laptop.
   
2. Step 2 Press any key a second time if the monitor goes from power-save to stand-by mode. Stand-by mode allows the screensaver to appear.
   
3. Step 3 Enter your user name and password into the login prompt if your computer requires a login. Press "Enter" to begin using your Dell computer.
   
4. Step 4 Change the display settings on your Dell monitor to prevent your monitor from going into power-save mode prematurely. Right-click anywhere on your desktop and choose "Properties." Click the "Screensaver" tab and press "Power." Beside "Turn off Monitor," choose a time amount from the drop-down list and press "Apply."
   

Usually hitting a button on the keyboard or moving the mouse works.

If it is really a problem go into your display settings through the control panel, access the power options and stop your monitor from going into powersave mode.

Monitor into Small Blue connector at back.
If Mouse and keyboard are Round and not Rectangular in shape then that's a PS/2 Mouse and keyboard. Purple goes into Keyboard slot at back. Green goes into Mouse at back. Watch for the design as the pins inside each one need to be inserted accordingly.
If they ARE rectangular then that is a USB connection. On the back connect the keyborad and mouse to the top two. Again, only going to insert one ways.

Sometimes, i can be the wiring, so check all of that. But apart from that. I don't know! Hope this helps!
DigicalJAI

Have you tried to disable the pwer saving mode and see what happens. What operating system do you have on this laptop please ?

Have you try to run PC in safe mode?
Please reboot your computer in Safe Mode by doing the following:
To go into Safe mode -- Press F8 key as soon as the PC restarts.
(You will have do again if PC starts in normal mode.)
On the black screen >>> Safe Mode With Networking(for internet Access).
On the login screen, please select Administrator as a USER to login.
Press 'YES' when you get the safe mode warning.