I'm considering creating some instrumental music. I don't care about connecting external stuff (keyboard, mic, ...), so I only require something I'll control with only a keyboard and a mouse. Is there any FLOSS suitable for a newbie like me?
It sounds like you want a sequencer.
I haven't used it but LMMS (Linux MultiMedia Studio) looks reasonable (if still young): http://lmms.sourceforge.net/
THE open source DAW is ardour. It is built on jack, a low latency audio driver daemon, and it has all stuff that you expect in a DAW, multi-track recording/editing/mixing. No windows support though, which shouldn't be a pain for open source enthousiasts, as jack offers support for most well-known audio interfaces.
... with only a keyboard and a mouse.
There are so many ways you can make some noise (er... music) with just a computer-keyboard and mouse. Concepts explained below are generic, but the softwares mentioned here run on linux.
Music Score Editors
You could use a music score editor to draw notes and compose music. Score Editors either use an internal synth or allow you to use a software synth plugin or soundfont.
Try: Muse Score, Denemo, Tux Guitar (write guitar tabs)
A sequencer lets you record (or write by hand) and arrange musical snippets in many ways. Most sequencers have a piano-roll-view for writing notes by hand, some might include a notation editor.
Rosegarden, Muse, Seq24, lmms (as Benji York suggested), Hydrogen (drum machine)
Try some Trackers too.
A Synthesiser takes the notes you feed and produces the sound accordingly. You can use these syths along with your Score editor/sequencer.
Qsynth, Fluidsynth, amsynth, Bristol
You could use some effects plugins to process the sounds produced by these synths. Try some LV2 plugins. Eventually you'll need some real DAW software to record and process this audio. Try Ardour
On a linux system you could connect these components together using Jack. Some linux distributions are tailor-made for media production, and come bundled with handful of Audio apps and synths. It's a good idea to begin with one of them. ex: Puredyne, Puppy Studio, Ubuntu Studio
Pure Data, Csound
Sorry, too lazy to add links. tip: google. Good luck!
Linux... keyboard and mouse... newbie...?
I'll second ananth.p's suggestion to try a tracker -- one of the easier computer music tools. It's essentially a standalone sampling synth / drum machine program with an old-school interface (see http://en.wikipedia.org/wiki/List_of_audio_trackers for screenshots and more info). Try MilkyTracker for starters.
If you find trackers too limited, try a sequencer. Think of it as a modular tracker -- you can connect it to all kinds of synths and effects via JACK (which is pretty complicated). QTractor is a relatively easy sequencer/DAW that nobody has mentioned. Seq24 is an old-school sequencer with a tracker feel. Check out LSD's video tutorials to see how it's used.
Audacity® is free, open source software for recording and editing sounds. It is available for Mac OS X, Microsoft Windows, GNU/Linux, and other operating systems. Learn more about Audacity... Also check our Wiki and Forum for more information.
The latest release of Audacity is 1.3.12 (Beta). This is our active "work in progress" version with our latest features. Documentation and translations into different languages are not quite complete. We recommend this version for more advanced users, and for everyone on Windows 7, Windows Vista and Mac OS X 10.6. See New Features in 1.3 for more information about the 1.3 Beta series.
Audacity 1.2.6 is our main release, complete and fully documented, but no longer under development. You may install Audacity 1.2.6a and 1.3.12 on the same machine.
Pair it with some free plugins and you're off and creating.
I'm not interested in MIDI (nor do I actually know what it is)
Moving right along. You're looking for something like Audiotool. It's free and completely browser-based. It's got drum machines, synthesizers, FX, and so on and so forth. Unfortunately, there aren't a lot of free and open-source options when it comes to doing what you want to do - sequence MIDI data into a virtual synth. LMMS is an option, yes, but it's kinda terrible IMO.
Oh, and there's Darkwave Studio. It is free and open-source, but it appears to be Windows only.
It would be helpful for you to do a quick Google search for terms that you don't understand before posting here. It's easier for us to help you if you are willing to help yourself.