Inspiron 530s won't boot up

Was it an add-on video card that was causing problems, or the on-board video?  Either way your problem is likely the result of the operating system trying to use the old driver for the new card.  If the card giving you the original problem was the on-board video (in other words, not a card at all) it may help to disable the video adapter in the device manager before you install the new card into the PCI-e x16 slot.  If it was another add-on card that you had to remove from the PCI-e x16 slot before installing the new one, you need to uninstall the card using the device manager before installing the new card.  Both of these actions help to make Windows load the plain VGA driver so that you can see what you're doing with the new card.

Once you have the VGA driver running you can shut the computer down, install the new card, check that you get a VGA low resolution screen on the new card when Windows has started, and then install the driver for the new card.  Your new card is probably working since you see the Dell start-up logo, and may see the initial Windows start-up screen as well.  These screens use a plain VGA display that doesn't make use of the higher resolutions available on the video card.

I forgot to mention that I plugged the new video card into the PCI express slot if that helps. Thanks

The original problem was the "on board" video not an add on video card. The problem is that I cannot disable anything or view device manager because when I start the computer I cannot see anything due to the lines on the display. The screen is completely covered and  you can't navigate anywhere. I can't tell if windows even loads.

One thing additional you can try to get the on-board video working again is to reset the CMOS.  The main board has a nickel-size lithium cell to keep the CMOS memory alive when the computer is off.  Remove all power, remove the lithium cell from the board for about five minutes, put it back in its holder, and try to start up again.  At some point while the cell is still out of its holder (and the power cord is still removed!), push the power button and hold it in for about fifteen seconds to discharge any remaining storage elements.  When the computer restarts, all its devices will be re-detected, which will occasionally get things working again.

If that doesn't help, put your new card back in the PCI-e x16 slot, connect the monitor to it, and start the computer.  While the Dell logo is still on the screen, press F2 to get to System Setup and check out the video adapter setting as requested earlier.  It should default to initializing a PCI-e card first, and if that is what you find you can leave it alone.  Escape out of System Setup and press F8 before Windows begins to load to get into safe mode.  If you miss it the first time, let everything settle, turn off the computer, and try again.  When you reach the Advanced Start-up menu, choose to start in Safe Mode.  Navigate to the device manager, click on the "+" on the left of Display Adapters to see what is available.  Double click the Intel Graphics adapter to bring up its properties screen.  At the bottom of the General settings you should find a box labeled Device Usage.  Use the drop down menu to select Do Not Use This Device - Disable.  Click OK until you are out of the settings and allow the computer to restart.  See if you now get Windows to start up in normal mode using the plain VGA driver on the new card.  If you do you can attempt to install the driver.

EDIT:  Re-reading your original post I note that you didn't get F2 to work at least one time around.  Sometimes it works better if you tap the key two or three times while the Dell logo is still visible instead of just pressing it once.