Hmm,
I would recommend that you clear your cache. if you are not sure how - go to your in game settings, Local Temporary Savings, then click the icon by "Delete local browser cache". This link that may help:
http://www.wikihow.com/Clear-Your-Browser's-Cache
Also, i am not sure if you are using the same browser on the different computers but try an alternate browser.
If these do not work then I would recommend that you check your supporting programs that Grepolis uses, example Adobe flash and similar programs and make sure they are current.
If all this doesn't work, then contact in game support and tell them what steps you have taken. They should be able to help from there.
Let us know how you make out.