My Dell PC's display is getting faulty day by day

It looks like one of the pixels in my display has started deteriorating and starting to give a look of a small glaring white pixel. I'm not sure if it will stop there or other pixels will also start to do the same. What I do except for replacing the whole display. BTW it's 3-year-old laptop?

 

Backing up any important data immediately should be your first concern. Be prepared for it to die eventually, even if it does not. You might want to be saving up for a new system. Replacing the screen in an older laptop, especially if it is low-end isn't usually worth the effort.

How much did you pay for that laptop?

 

Uhh you do realise its probably just the LCD, even if it's GPU, you can still recover data by taking the HDD out.

OP: Does this happen if you connect an external display? If so then GPU might be on the way out, if not it's just the LCD

Although it is a good idea to backup important data anyway...
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Play this at 2x speed. (full screen) maybe keep doing it for 8 hours maybe.
Might help unstick that pixel.

 

Backupping is best practice regardless of hardware status (it's also easier to backup a healthy machine).

Especially if you plan to give the laptop to a repair shop or want to attempt a repair on your own, setting the data aside and optionally wiping the laptop are good things to do.

Michaelflat's suggestion is a nice first step before going for more in-depth solutions. If the cause is mechanical damage, it's quite possible that it will increase in size over time. It might also be better to replace the LCD panel because stray currents may damage other components over time.

If you want to DIY, you might try to look for "YourLaptopExactModel disassembly" videos on YouTube. You watch the right video 1 or 2 times, then if you feel confident you watch it again, pausing while removing and disassembling the screen assembly. Manage your screws and components: use a multi-compartment box/tray, like an egg box or chocolate candy box tray.
Now you can check the exact LCD panel model (it's not uncommon for one laptop to be fitted with many different monitors, with different connectors even).
You then head to eBay and look for the right panel from a decent vendor - screens are very fragile, you want a seller that knows how to package and ship them. If you are very confident, you might select a better panel than what came with your PC. This requires a lot of attention and careful searching though.
Then you carefully fit the new panel, keeping the video in sight for reference.

Dells are usually DIY friendly, but that may vary by model. Price will be anywhere from $50 to $200 depending on panel quality and availability. Small Phillips screwdrivers and some expired credit cards/guitar picks are usually the only required tools. Expect 60 to 180 minutes total work time depending on procedure complexity, skill level and general understanding of what you're doing (complete disassembly videos strip apart the full machine, but you want to limit this to the screen as much as possible, if possible).

Laptop screens and screen connectors are extremely frail: don't rush and seek guidance before breaking anything!

 

Probably save all your files on an memory stick and reboot it or put it in to safe mode
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Unless it is just the batteries in your screen that are diying out

 

I do hope your joking, the batteries in a screen don't run out, there aren't any! If there was a power fault, only the back-light would be affected, and so it would be dimmer.