Same problems on a fresh Mandrake 7.0 install
No SSL

[mod_perl]
perl Makefile.pl APACHE_SRC=../apache_1.3.11/src USE_APACI=1 EVERYTHING=1 PERL_MARK_WHERE=1 PERL_SSI=1
make
make install

[apache]
./configure --with-layout=RedHat --activate-module=src/modules/perl/libperl.a --enable-module=all -enable-shared=all -disable-shared=perl
make
make install

(of course NO PROBLEMS here, none compiling, none running Apache)

[php 3.0.14]
./configure --with-apxs=/usr/sbin/apxs --with-config-file-path=/etc/httpd/conf --with-gd --with-xml --with-mysql

MySQL 3.22.32 installed from source RPM compiled on the same system.

run /usr/sbin/httpd -X or attempt to start Apache with apachectl:
Segmentation fault (core dumped)
 
# gdb /usr/sbin/httpd ./core
(reads symbols)
#0  0x4038b0f8 in ?? ()
(gdb) set args -X
(gdb) run
Starting program: /usr/sbin/httpd -X
Cannot access memory at address 0x403044d4  


ANYONE HAVE ANY IDEA WHAT'S GOING ON?  (starts pulling hair and stuff out!)

Just Apache 1.3.11 and PHP 3.0.14:
(no I don't use NIS/YP)
Pretty much the same compile options...

#0  0x4038d246 in nis_getservlist (dir=0x80d0160 "p\001\r\b??\030@?#\016\bI")
    at nis_getservlist.c:70
70      nis_getservlist.c: No such file or directory.
(gdb) bt
#0  0x4038d246 in nis_getservlist (dir=0x80d0160 "p\001\r\b??\030@?#\016\bI")
    at nis_getservlist.c:70
#1  0x4016b70f in pmap_getport (address=0xbfffd5bc, program=100007, version=2,
    protocol=6) at pm_getport.c:88
#2  0x40169b09 in clnttcp_create (raddr=0xbfffd5bc, prog=100007, vers=2,
    sockp=0xbfffd598, sendsz=0, recvsz=0) at clnt_tcp.c:145
#3  0x40384a2f in __yp_bind (domain=0x40393a40 "Jewel.SomeSites.com",
    ypdb=0xbfffd608) at ypclnt.c:149
#4  0x40384d60 in do_ypcall (domain=0x40393a40 "Jewel.SomeSites.com", prog=3,
    xargs=0x4038424c <xdr_ypreq_key>, req=0xbfffd65c "@:9@\020\004<@\006",
    xres=0x40384310 <xdr_ypresp_val>, resp=0xbfffd650 "") at ypclnt.c:267
#5  0x40385112 in yp_match (indomain=0x40393a40 "Jewel.SomeSites.com",
    inmap=0x403c0410 "passwd.byname", inkey=0x80c3454 "nobody", inkeylen=6,
    outval=0xbfffd6e0, outvallen=0xbfffd6e4) at ypclnt.c:430
#6  0x403bd2d9 in _nss_nis_getpwnam_r (name=0x80c3454 "nobody",
    pwd=0x4018e0a0, buffer=0x80d6be8 "nobody", buflen=1024, errnop=0x4018cc40)
    at nss_nis/nis-pwd.c:231
#7  0x4012b9bf in __getpwnam_r (name=0x80c3454 "nobody", resbuf=0x4018e0a0,
    buffer=0x80d6be8 "nobody", buflen=1024, result=0xbfffd788)
    at ../nss/getXXbyYY_r.c:182
#8  0x4012b211 in getpwnam (name=0x80c3454 "nobody") at ../nss/getXXbyYY.c:137
#9  0x806d204 in ap_uname2id ()
#10 0x8059c48 in set_user ()
#11 0x8054e7d in invoke_cmd ()
#12 0x80558a1 in ap_handle_command ()
#13 0x805593d in ap_srm_command_loop ()
#14 0x8055d94 in ap_process_resource_config ()
#15 0x80566fc in ap_read_config ()
#16 0x80604d0 in standalone_main ()
#17 0x8060dfc in main ()
#18 0x400c39ee in __libc_start_main (main=0x8060a64 <main>, argc=2,
    argv=0xbffffa74, init=0x804e828 <_init>, fini=0x8096134 <_fini>,
    rtld_fini=0x4000a570 <_dl_fini>, stack_end=0xbffffa6c)
    at ../sysdeps/generic/libc-start.c:90       

I've also tried this with the binary rpms from the MySQL people, same result.
#0  0x4038a0f8 in ?? ()
#1  0x40179313 in __getservbyname_r (name=0x40426a36 "mysql",
    proto=0x40426cd0 "tcp", resbuf=0x401a5f5c, buffer=0x817e190 "mysql",
    buflen=1024, result=0xbfffd6e8) at ../nss/getXXbyYY_r.c:182
#2  0x401791c5 in getservbyname (name=0x40426a36 "mysql",
    proto=0x40426cd0 "tcp") at ../nss/getXXbyYY.c:137
#3  0x403ede5a in php3_minit_mysql (type=1, module_number=9)
    at functions/mysql.c:258
#4  0x403ced2a in module_startup_modules () at internal_functions.c:533
#5  0x403c79a7 in php3_module_startup () at main.c:1237
#6  0x403c52e0 in php3_create_dir () from /usr/lib/apache/libphp3.so
#7  0x8080b5c in ap_single_module_configure ()
#8  0x8061686 in load_module ()
#9  0x807f2ae in invoke_cmd ()
#10 0x807fc11 in ap_handle_command ()
#11 0x807fcad in ap_srm_command_loop ()
#12 0x8080104 in ap_process_resource_config ()
#13 0x8080a6c in ap_read_config ()
#14 0x808a840 in standalone_main ()
#15 0x808b16c in main ()
#16 0x400da9ee in __libc_start_main (main=0x808add4 <main>, argc=2,  argv=0xbffffa84, init=0x8060394 <_init>, fini=0x8129754 <_fini>,
    rtld_fini=0x4000a570 <_dl_fini>, stack_end=0xbffffa7c)
    at ../sysdeps/generic/libc-start.c:90

Please, if anyone can tell me if it's possibly a certain library or something, let me know and I will rip apart my system if I have to in order to get it working!!

Make sure your mysql client library is not linked against pthreads.  Check using: ldd libmysqlclient.so
Try a current snapshot from snaps.php.net and let us know if you are still seeing these problems.