Yes, it is possible to run two MySQL instances on one PC, but I'd suggest upgrading, because MySQL 4.1.22 is insanely old. That is unless you have legacy applications that can't handle newer MySQL protocols or new password hashing algorithm.
If you still want to run another instance alongside old one, you'll have to change listening port number. It should be available during setup.
MySQL upgrading is a multi-step process on Windows and can't be accomplished without some downtime.
Here's how to do it, step by step:
1. Export all databases from old MySQL using mysqldump or your favourite MySQL management tool
2. Stop and remove MySQL service, if it was installed
3. Install new version of MySQL
4. Set up users and permissions (can be done during installation)
5. Import data dumps from old database
There are other ways to do upgrades, but I find this less painful.
Another option would be to install MariaDB which offers data and settings migration from MySQL, but it might not be able to migrate data from really old MySQL versions. If so, you should proceed same as with MySQL upgrade.