Lightroom colors are different between computer and develop mode

It does no harm as long as it's not set as default, but you might as well remove it.

That's strange. Close all color management dialogs. Then go to 

C:\Program Files (x86)\Common Files\Adobe\Color\Profiles\Recommended

Copy AdobeRGB1998.icc to C:\Windows\System32\spool\drivers\color

Then go to color management again and check.

Scroll down to the bottom, and you should find Adobe RGB (1998)

Like I said, you should use Adobe RGB because your display is wide gamut.

This may be close enough, but for complete color accuracy, use a hardware calibrator.

The Dell XPS has a wide gamut screen, which means that applications without color management will display images over saturated.  So if you're using the Photos app (not color managed), this is unavoidable. With a wide gamut screen, you must only use color managed applications to view your work.

The only native color managed application on Windows is the Windows Photo Viewer, which will display correct colors. It's hidden by default, do a search for it.

previous images that were edited on my old laptop look good in the photos viewer, but look completley washed out in Lightroom. So I am now having the opposite effect as well. 

I can only guess why this happens – maybe your old computer had a defective monitor profile, which caused you to (unknowingly) edit them to be washed out. It could also be that the monitor profile on your old computer was correct, and the one on your new computer is wrong.

I suggest that you start out by calibrating the screen with a hardware calibrator, which will also create and install a custom monitor profile, which accurately describes your monitor. That way you can be certain that images will display correctly in color managed applications. like Lightroom.

If you don't have access to a calibrator, you can (temporarily) set the monitor profile to Adobe RGB.

This will almost certainly be better than your current profile, Dell profiles are notoriously bad.

Close Lightroom and any other color managed applications.

Then go to Control Panel > Color management, add Adobe RGB and set it as default.

In the screenshot below sRGB is used, but since you have a wide gamut screen, use Adobe RGB.

I should also mention that previous images that were edited on my old laptop look good in the photos viewer, but look completley washed out in Lightroom. So I am now having the opposite effect as well.