This is a loaded question as we know very little about the source for the import and what errors might be showing.

Let me start with the fact that the import must match the format required by Sage to import the COA effectively. A missed comma or an extra comma can make the process hick up and not complete the import. To solve some of this I have a set practice of exporting a COA to Excel to start. If this is a new company set up I would add three or four accounts manually so that you have different options with them. Then you would have something to export to Excel. Open the Excel file and do not make any changes to the first line. Now you will have the format available and you should make sure all of your accounts follow the same coding. Once you have the spreadsheet ready to upload, give it a try. The program will let you know which accounts worked and which ones did not work. Print this notice so you have the information and then modify those specific accounts and try again. The errors provided by the import feature are very important when trying to resolve the issue.

Give it a try and then post back. 

Is it possible you created the new company file WITH a chart of accounts instead of without any?  If so, then the import will not import any account with an account number that already exists.  The import will not overwrite any account that exists.