F#, 382 chars
I compressed two letters from each row into an ascii-printable byte, and handled space and exclamation point specially.
let s,(!)=stdin.ReadLine(),printf"%s"
for n in 0..4 do
for c in s do if c=' '||n=3&&c='!'then !" "elif c='!'then !"!!! "else for x in 0..3 do printf"%c"(if(Array.collect(fun b->let B n=int b&&&n=0 in[|(B 64)||not(B 8);B 32;B 16;true;B 4;B 2;B 1;true|])"wvwuwTUwvwUUWUEDEiTwUUBURQwEfWidWWVrUrrUEDUmTUTuZUr\\WvtuwWUturruw"B).[n*104+(int c-int 'A')*4+x]then ' 'else c)
!"\n"
Sample I/O below:
HELLO WORLD!!!
H H EEE L L OOO W W OOO RR L DD !!! !!! !!!
H H E L L O O W W O O R R L D D !!! !!! !!!
HHH EE L L O O WWW O O RR L D D !!! !!! !!!
H H E L L O O WWW O O R R L D D
H H EEE LLL LLL OOO WWW OOO R R LLL DD !!! !!! !!!
ABCDEFGHIJKL
AAA BBB CCC DD EEE FFF GGG H H III JJJ K K L
A A B B C D D E F G H H I J K K L
AAA BBB C D D EE FF G G HHH I J KK L
A A B B C D D E F G G H H I J J K K L
A A BBB CCC DD EEE F GGG H H III JJJ K K LLL
MNOPQRSTUVWXYZ
M M N N OOO PPP QQQ RR SSS TTT U U V V W W X X Y Y ZZZ
MMM NNN O O P P Q Q R R S T U U V V W W X Y Y Z
M M NNN O O PPP Q Q RR SSS T U U V V WWW X YYY Z
M M N N O O P QQQ R R S T U U V V WWW X Y Z
M M N N OOO P QQQ R R SSS T UUU V WWW X X YYY ZZZ