Getting a VCD to play on a PC can be difficult if you don't know what your doing.
The .dat file you saw, does contain the video and audio data you created.
If you have a media player such as PowerDVD you might be able to get your CD-R to play upon insertion or via the players 'Select Source' option.
If you want play the .dat file with the WinMedia player you will have to force the player to read the file.
To do this, find the file on the CD. Right click on it. Go down to 'open with'. 'Choose Program' and then select the 'Windows Media Player'.
If you are currently using Nero's CD Burning ROM software, you might find it easier to create your VCD's using Nero's Vision Express instead. As the interface is a fair bit simpler to use.
There's no easy solution to your situation.
As, if you decide to go for DVD. You'll most probably find that not everybody who doesn't have a DVD player but who has a PC, has a DVD rom drive in it - I hope that makes sense!
You could however, create 2 CD versions of your creation. One CD using the VCD format for use in DVD players. And another CD (data format) for use in PC's. And, it's still a more cost effective option than DVD.
That's not to say you can't create a CD that will run on both a DVD player and a PC because you can. One way of doing so is to burn the data on it twice (as a .dat files etc and as raw .mpg files). I do, do it commercially but I don't know of any public software that is available and at what cost.