Not tested but try it:

///////////////////////////////////////////////
// startup splash screens
// script written by william mason May 02,07
///////////////////////////////////////////////
bmap splash1 = <splash1.pcx>;
bmap splash2 = <splash2.pcx>;
bmap splash3 = <splash3.pcx>;
bmap splash4 = <splash4.pcx>;

panel splash_1(){bmap = splash1;layer = 25;}
panel splash_2(){bmap = splash2;layer = 25;}
panel splash_3(){bmap = splash3;layer = 25;}
panel splash_4(){bmap = splash4;layer = 25;}

panel* screen_syn = splash_1;

starter splash_start
{
freeze_mode = 1;
WHILE (1) {
WHILE (temper < 48) {
screen_syn .visible = on;
temper += time;
IF (KEY_SPACE == 1) { screen_syn.VISIBLE = OFF; return; }
wait (1);
}
screen_syn.VISIBLE = OFF;
IF (screen_syn == splash_4) { screen_syn = splash_1; continue; }
IF (screen_syn == splash_3) { screen_syn = splash_4; }
IF (screen_syn == splash_2) { screen_syn = splash_3; }
IF (screen_syn == splash_1) { screen_syn = splash_2; }
wait (1);
}

freeze_mode = 0;

// remove bmaps from memory
bmap_purge(splash1);
bmap_purge(splash2);
bmap_purge(splash3);
bmap_purge(splash4);


P.S. The bracket for closing the starter is missing!

EDIT: @Germanunkol You were faster, but in your code the loop will go on until he's finished and not break at once when space is pressed