Via Winchester73 at LandzDown who ran into the issue when troubleshooting for someone he was helping.
From Microsoft Security Essentials error stutters Windows XP systems
The issue starts as soon as Windows XP system is booted. The MSE error read: “MsMpEng.exe application error. The instruction at “0x5a4d684d” referenced memory at “0×00000000″ The memory could not be read”.
The MSE issue arose on the 16th with a faulty update.
You might wish to review this: How to manually download the latest definition updates for Microsoft Security Essentials
1) Boot into safe mode with networking
2) Manually type http://go.microsoft.com/fwlink/?LinkID=87342
into the address bar to download the 32-bit definition file.
3) The computer should return to normal upon reboot.
Winchester73 also recommended the following: a complete shut down of the computer, then power it back up (not a re-start, you want the POST provided by a cold boot). Don't touch any keys (even to close the MSE nag screen about XP) until after the hard drive stops doing its thing and the light goes out. Then click away, open things, close things, see if everything works "normally" again ...
The above solution has already helped someone else who is not in a position to replace her computer until later this year.