Hi Justapen,
What you’re describing is certainly possible.
Here is how I would go about it.
1) Take my ExpressionEngine 1.6.9 site and get it setup and working locally.
2) Update locally from 1.6.9 to ExpressionEngine 2.4.0.
So, for getting your old site to work locally
1) Make sure you have everything backed up. So, all files, and databases. Which it sounds like you already did.
2) On my local setup, take the files I backed up and put them in my local setup, and import the EE database into my local db.
3) Update any paths and settings that have changed from the remote server to the local setup. Things like your database settings, url paths, etc.
4) Now you should have your old site running ExpressionEngine 1.6.9 locally.
Now that that’s up and running locally, you can follow the Upgrading from 1.x to 2.x instructions to bring your 1.6.9 site up to 2.4.0. Remember to check the add-ons you’re using and make sure they’re EE2 compatible.
Let me know if you have any more questions.
Thanks.