You don't want to transpose as all your column data remains in columns.
You want multiple output rows per input row. This can be done by using several output statements in a data step;
[pre]
data IN;
ID='1'; hospital='a'; admit_date='01jan2000'd; lab_date='01jan2000'd;
TEST1='gluc'; RESULTC1='-40';RESULTN1=2;
TEST2='chol'; RESULTC2='208';RESULTN2=45;
TEST3='urea'; RESULTC3='4'; RESULTN3=415;
run;
data OUT;
length TEST RESULTC $20 RESULTN 8;
drop TEST1 RESULTC1 RESULTN1
TEST2 RESULTC2 RESULTN2
TEST3 RESULTC3 RESULTN3;
set IN;
TEST=TEST1; RESULTC=RESULTC1; RESULTN=RESULTN1;
output;
TEST=TEST2; RESULTC=RESULTC2; RESULTN=RESULTN2;
output;
TEST=TEST3; RESULTC=RESULTC3; RESULTN=RESULTN3;
output;
run;