OK, forget about diodes for audio. They are useless on many levels. Normal silicon diodes have a 0.7V forward voltage drop which will kill most of the audio signal and leave only the peaks. Schottky diodes bring that down to ~0.3V, but it will still distort the signal heavily. Besides the fact that diodes only let current go in one direction (DC) and audio is AC! Unless you bias the audio on DC level, diodes are useless.
To mix audio from several sources simply using resistors is one way. Connect two resistors to the sources and the other ends together to the output. Grounds connected all together of course. Experiment with resistors close to the impedance of the audio signals (10Kohm is typical I believe).
Headphone splitters simply connect both inputs together. If one is driving low and the other one is driving audio, this will short the audio out if the impedance is 0 (which it may very well be with some audio sources). In this case the computer probably has a lower impedance than the DVD player, and grounds its signal. Resistors will not allow either source to blatantly affect the other, although there will be some differences. If one source mutes the other while not playing anything or turned off, it is applying a DC voltage, so use capacitors to stop it. Experiment with the values, but I believe it should be on the uF scale, try 1, 10, and 100uF and see what you like best. Lower values will tend to kill bass / lower frequencies, while higher values will take more time to settle to DC changes (and are larger physically).
If one source is significantly louder than the other and you can't compensate using volume controls, and/or you want to mix them, use variable resistors as volume controls. A set of two resistors, one from the input, another one from ground, joined together at a common point that you can connect to your mixer, will serve as a voltage divider. Varying the relation between the values will vary the output voltage, where the output will be R1/(R1+R2) times as loud as the input. So, if R1 and R2 are the same, output volume will be 50% (linear scale, so likely you will not perceive it as 50% since the human ear is logarithmic. Experiment.). A variable resistor (potentiometer) would be connected with left to source, right to ground, and center to mixer. Be sure to use values close to the impedance to minimize issues.
The audio mixer circuit shown above is using exactly that: resistors to mix the audio, plus capacitors to kill the DC level (you might want to try using them too), and two op-amps as line amplifiers. If the sound level is too low, try using the op-amps too, but then you'll need a power source ( a simple wall-ward adaptor will work)
So, to summarize: diodes are a no-no. Resistors mix audio. Capacitors make sure that what gets through is only audio and not killer DC signals (which can kill the other audio source). So, capacitors and resistors are likely what you want: caps to prevent the PC from killing the DVD when idle, and resistors to mix both signals into one. You could also try only capacitors with no resistors - not sure how that would turn out, but if you try it it would be interesting to hear the results.
I'm not an audio master BTW, so if anything that I've said doesn't work I take no responsibility

(I'm more used to the digital domain, but those tips about audio signals should about work for the most part).
Oh, I'm new here

You'll probably see me quite a bit on the electronics forum