Is there any software that would allow computer and PDA operating system to recognize each other?

Windows 7 is a very user friendly operating system. As you said that you are using a old Palm Zire 31 PDA and your computer didn’t connect to the PDA and also not able to find the driver software over the internet, so I want to tell you that windows 7 operating system supports almost all driver software and easily connected to any other software device. But if you are facing problem with the connection, I would suggest you to please download the latest windows 7 supported PDA driver software from the internet. And then install the driver on your computer system and then you are able to connect your PDA device to your Windows 7 based computer system. Apart from this, there are lots of other third party software available on the internet which give you the driver software on free basis and certain websites provide you the driver software on paid or free basis.