Assuming that you are able to log on as an administrator then you should be able to install and run both Apache and the ActiveState Perl distribution. If you are restricted then the chances are that your user account is not part of the local administrators group. Have a word with the IT function in your company, explain the situation and ask them to try and do make you a local admin account.

The slightly more in depth approach is to install Apache and a Perl distro on a server that you can control and then copy the resulting directory structures. This will work on the basis that both applications were initially targeted at the Unix community and as such make minimal use of the windows registry. Just make sure that the location to which you copy the directory structure is the same as on the server. e.g. The location of Perl should be C:\Perl on both computers.