Can I split my screen so I can use two computers at the same time?

Although USER has the right idea in that you DON'T need two monitors.  You can get a KVM switch which woudl allow you to hook both up to one Monitor, Keyboard and mouse, but you would also need a connection that would allow data transfer between the two computers. I would simply pull the HDD out of the NEW computer and mount in the OLD computer as a second drive.  Drag and drop all your documents, profile, settings, everything.  Then remove the drive and place in the new computer. Not as difficult as it sounds.  Just be sure to unplug the power when working internally.  

So many impractical answers.   To access two computers on one monitor you just access the secondary PC with remote desktop.  Boom two computers on one Monitor.  *mind blown*  If you enable remote drives within remote desktop you can start transfering the data directly to the new PC.

In order to switch between the two different computers with one monitor, you need to access the internal menu of the monitor and change the input. ... Certain ultrawide screens can display the input from two different computers at the same time, in a split-screen configuration.

You'd need either a manual VGA (or HDMI) switch, or an expensive video box if you wanted to see them both at once. Since you're only doing this once, I'd just swap the cable between the two PCs when you wanted to look at the other screen. 

I did it on my old laptop. You can check this article https://digioner.com/how-to-use-your-laptop-as-a-m... I think it will solve your problem.

why  , after all you cant use 2 computers at once  , to transfer data you a serial port not a monitor anyway , seems you dont have any idea , do you .

No, you can't do that.   Transfer your data to an External Hard Drive.

Although USER has the right idea in that you DON'T need two monitors.  You can get a KVM switch which woudl allow you to hook both up to one Monitor, Keyboard and mouse, but you would also need a connection that would allow data transfer between the two computers. I would simply pull the HDD out of the NEW computer and mount in the OLD computer as a second drive.  Drag and drop all your documents, profile, settings, everything.  Then remove the drive and place in the new computer. Not as difficult as it sounds.  Just be sure to unplug the power when working internally.  

There is no way to display two computers on a single monitor.  

However if both computer are hooked to the same wifi network, you should be able to make a remote connection from the new computer to the old one.  That will allow you to open the contain of the old computer in a File Explorer window on the new computer.  You will be able to see all the files and folders and then copy from that window to the new computer.

Open a File Explorer window.  In the bar at the top type in

\\name_of_the_old_computer\c$

The old computer's C: will open in the window.

Then you copy whatever you want form just like you would copy files between any two folders on your computer.

Not without extra equipment.  

Switch between computers by swapping cables.

Borrow a monitor.

Use a TV with appropriate input.

Most data can be transferred with a thumb drive, the cloud, by cable, or pulling the old drive.