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Ok, the first and most important thing you need to know (in case you don't already know) is that Inkscape can only use fonts which are installed on the computer. So if you normally download fonts to some particular location or directory, you might be able to find the original font, assuming you would be able to recognize it on sight (since you don't remember the name). Maybe it's just not installed on the new computer, and you just need to install it, assuming you can find it?
If the font isn't installed on the computer, then when you open the file, Inkscape does substitute another font. I don't know how it decides which one to use, and Inkscape does not notify you. Since I don't have the font you mentioned installed, Inkscape is showing me Century Gothic font. (Depending on how you transferred fonts from old computer to new, the particular font might not be installed, and that's why Inkscape substituted another font.)
Unless you can find the original font, I'm afraid you'll have to re-do at least part of the logo. When you do, I suggest not to use Flowed Text.
Flowed text is created when you drag out a text box, with the Text tool, and then start typing. To create regular font, just click once on the canvas, and start typing. Later, you can move it to wherever you want it. (Flowed text is really only visible in Inkscape. If you put the logo on the internet, for example, the text would be missing.)
Just so I'm clear, the JPG you attached is showing the original font that you want, right? Well, it looks like a very basic type of font. It should not be so hard to find something similar. If you can't remember the name of the original font, or where you got it, I don't know how you can avoid re-doing at least the text part of the logo.
Oh, actually there are a couple of different fonts. I do see that SansLuzBook font..... Hhmm, but there doesn't seem to be any actual text in that font. I only see it referenced in the XML editor, but the status bar says it's an empty text box. But you said that's not the font you want anyway, right?
I don't know. The only option I can see, if you can't find the font wherever you downloaded it, is to find another new font to use. It shouldn't be very hard, since it looks like a fairly basic type of font. If you're careful with the font choice, you wouldn't have to re-do the overlapping circle Os.
