How do I open a 2004 turbotax return without the program?

You can’t open a tax file without the program. As stated above, you can’t order a transcript from the IRS that old. 

If you have a .tax or .tax20xx file you need that year's Desktop program installed to open it.

Turbo Tax doesn't have programs older than 3 years.  You might be able to find one on Ebay or Amazon or somewhere but you wouldn't be able to update it or download the state program.

You could try the TaxPrinter service (not connected with Turbo Tax) to convert a .tax file to pdf at

http://www.taxprinter.com

They might be expensive and it is probably not safe to email tax returns back and forth.

The IRS does not have transcripts going back to 2004. it like turbotax only keep records for the last 6 years. 

Even if you can get the 2004 TTX program, I seriously doubt it would work on any of today's operating systems.