Running Elite with DOSBox
DOSBox sets up a DOS environment on your PC, with all memory issues etc addressed. The DOSBox website has all the details, including a list of all the games it will run, but for the basic purpose of getting Elite to run, all you need is here at FrontierAstro.
Firstly, create a folder on your C drive called "PCElite". Then download the game from Ian Bell's Elite Page and extract the zip file to C:\PCElite. Rename the file to "Elite" if necessary
Download the DOSBox Installer and install the program to the default location, as shown above
Download and extract this small zip file and put the batch file in your C:PCElite folder.
Now run the batch file and, with a bit of luck, Elite should load up and run. If it doesn't then its possible you didn't place the files exactly as specified above. If that's the case, move them as appropriate or amend the batch files so that they match up with the Elite and DOSBox locations.