Hi Jay,
Sorry - I'm a little confused, I thought that you had uploaded PowerStore to your remote site (with 1&1).
To run PowerStore as a 'working' store, yes - it will need to be uploaded to hosted space on a remote server, - WebAssist recommends 1&1 as a hosting provider - so you may just need to renew or re-activate your hosting plan to get going again.
If you just want to get used to PowerStore or do a little prepatory work on it, you can install it on your local machine provided you have set up a testing server and can process dynamic (PHP) pages. If you could let us know a bit more about your situation/setup perhaps we can help out a bit more easily!