"c:/windows/system32/explorerframe.dll is either not designed to run on Windows or it contains an error"

You can try the following methods:

1. After you see the cursor (maker sure it's moving), try this:

Press Ctrl+Alt+Delete -> click on Start Task Manager. Click on File -> New Task (Run...). Type cmd and press Enter. Now, type the following commands:

cd %SystemRoot%\System32

runas /user: CMD.exe

Type your user account password. Kindly note that if you don't have password, this method will not work.

Once you're in the cmd with administrative privilege, type the following:

sfc /scannow

If this method is not working, try method 2.

2. Perform in-place upgrade with Windows installation disk. Refer the link for more information:

http://support.microsoft.com/kb/2255099/en-us

What version of Windows do you have? 
Do you have a Windows installation DVD? 
Can you boot into Safe Mode (tap F8 1-2 times per second BEFORE the Windows screen appears - as soon as the Dell logo appears)?

1. After you see the cursor (maker sure it's moving), try this: Press Ctrl+Alt+Delete -> click on Start Task Manager. Click on File -> New Task (Run...). Type cmd and press Enter. Now, type the following commands: cd %SystemRoot%\System32 runas /user: CMD.exe Type your user account password. Kindly note that if you don't have password, this method will not work. Once you're in the cmd with administrative privilege, type the following: sfc /scannow

I don't have a password, so it's there any other way to open a command prompt as administrator without access to the shortcut?

What I'm trying to say is that I can't right click the shortcut icon. There is no shortcut icon. Just a black screen and a cursor.

Simply right-click the cmd/Command Prompt icon/shortcut and Run as Administrator.  An account password is not required.

You don't need a password if you open it the "easy" way.

You tried what?  Safe Mode?  Did you make it to the menu, where you select Safe Mode?  or could you not get a menu when trying to press F8?

What version of Windows do you have? 
Do you have a Windows installation DVD? 

I couldn't get a menu.  I have windows 7 and the laptop didn't come with a disc.  

As soon as the Dell logo appears, start hitting the F8 key as fast as you can.

I tried that, it was audio suggested to me to try f10 and f12. None of those did anything.  It just booted normally.  Well, not normally, it still dies the whole black screen thing.  You know what I mean.  

That's why I said "The post indicated he could not log in, so this is not an option"! 

From that same post:

What version of Windows do you have?  Do you have a Windows installation DVD?  Can you boot into Safe Mode (tap F8 1-2 times per second BEFORE the Windows screen appears - as soon as the Dell logo appears)?

Kindly provide the Windows edition (like Home Premium or Ultimate) and architecture (32-bit or 64-bit), so that we can assist you accordingly.

Home premium 64 bit.

You are infected with malware and need to reinstall from scratch.