Keep this in mind as you read... I have no experience with Linspire, and am no immediately sure what it's based on or similar to...
So, knowing that, it sounds like other people have basically told you that you'll need to compile your own programs.
Don't worry, it's easier than you'd think (provided you have a working bundle), even for someone with little or no programming/linux knowledge.
Usually, what you'll want to do in this situation, is the following (assuming it's a trusted package):
Unpack the .ark, .tar.gz, .bz2, or whatever it may be, into any place there's room for it, and you'll remember where it's at, and all of that kind of thing.
Once it's done, there will almost always be a 'configure' file in there if you do a ls (dir equivalant from DOS, well, ls -al is closer, but that's another post).
Once you find it (most often it will be in the root of the unpacked items, sometimes it will be in the src directory...depends on the bundler) you will want to type this on the command line: ./configure
What that does, is execute the configuration script, which will then prepare what's called a Makefile tailored to your machine's needs.
When that is done (assuming there were no dependancy failures or anything), you will probably want to stay in that same directory, and type "make" at the command line. This will compile the program, and get it ready for use.
Once that is complete (again, assuming no errors...if there is one, it should be easily spotted by "error ***" or something followed by a detail of the error), you can try switching to root, and typing "make install". It may tell you "No rule to make 'install', or it may start doing some things.
-If it starts doing things, it's placing the executable into somewhere appropriate (like /usr/bin, or /usr/local/bin), and placing any other files it needs to so it can run properly.
-If doesn't do anything, then you can probably try just runing it from the command line there by typing ./<executable name>. The name will be what is built by the makefile, and is usually very similar to the name of the package you downloaded, minus any version numbering. This may or may not work, it depends, but it should hopefully be close.
Okay...if you're not scared off by now, then hopefully you have something you can run. If not, or if there's anything I've forgotten (doing this all from memory, but it should be fairly close), please ask/correct me about/with it.