Not able to ping DMZ port on Firewall from the switch.

What does "show interface vlan 102" show?
Maybe you didn't create the vlan in the vlan-database and the interface is down?

vlan102 should be up. See the result:

ColoC3750X#sh interface vlan 102
Vlan102 is up, line protocol is up
  Hardware is EtherSVI, address is 4403.a749.b345 (bia 4403.a749.b345)
  Internet address is 10.10.2.2/24
  MTU 1500 bytes, BW 1000000 Kbit, DLY 10 usec,
     reliability 255/255, txload 1/255, rxload 1/255
  Encapsulation ARPA, loopback not set
  Keepalive not supported
  ARP type: ARPA, ARP Timeout 04:00:00
  Last input 00:00:57, output 00:12:56, output hang never
  Last clearing of "show interface" counters never
  Input queue: 0/75/0/0 (size/max/drops/flushes); Total output drops: 0
  Queueing strategy: fifo
  Output queue: 0/40 (size/max)
  5 minute input rate 0 bits/sec, 0 packets/sec
  5 minute output rate 0 bits/sec, 0 packets/sec
     16993 packets input, 2604456 bytes, 0 no buffer
     Received 0 broadcasts (0 IP multicasts)
     0 runts, 0 giants, 0 throttles
     0 input errors, 0 CRC, 0 frame, 0 overrun, 0 ignored
     675 packets output, 45418 bytes, 0 underruns
     0 output errors, 1 interface resets
     0 output buffer failures, 0 output buffers swapped out

As earlier mentioned, the other switch (Winston-3750sw) is able to ping the DMZ interface without a problem.
Here is the result for sh ip arp: (10.10.2.1 is the DMZ interface ip. Is everything ok?)

ColoC3750X#sh ip arp
Protocol  Address          Age (min)  Hardware Addr   Type   Interface
Internet  10.10.2.2               -   4403.a749.b345  ARPA   Vlan102
Internet  10.2.6.14               -   4403.a749.b343  ARPA   Vlan60
Internet  10.2.4.14               -   4403.a749.b341  ARPA   Vlan40
Internet  10.10.2.1              36   001e.c9b2.788b  ARPA   Vlan102
Internet  10.2.5.14               -   4403.a749.b342  ARPA   Vlan50
Internet  10.2.0.1               73   0022.91b8.5bc8  ARPA   Vlan100
Internet  10.2.5.20             184   0cc4.7a53.9ec9  ARPA   Vlan50
Internet  10.2.5.18               1   0cc4.7a1f.30ec  ARPA   Vlan50
Internet  10.0.6.57               2   0022.91b8.5bc8  ARPA   Vlan100
Internet  10.10.2.141           138   0015.5d02.f609  ARPA   Vlan102
Internet  10.2.0.199              -   4403.a749.b344  ARPA   Vlan100

I do not see an arp for 10.10.2.1 when you do the ping did you try sourcing it from VLAN102 you shouldn't have too, but worth a try.  

As for why the other switch can ping the IP Address by the diagram it is going through the firewall to do so, not via the other switch since 102 is not carried on the trunk and it doesn't have an interface in that vlan.

on the ColoC3750X

can you also do a show VLAN
and sho arp dyn int g2/0/21

Thanks

"I do not see an arp for 10.10.2.1" ?  Didn't you see it listed? The fourth from the top. Isn't it for 10.10.2.1?

How to ping with sourcing from VLAN102?

Here is the result of sh vlan:
ColoC3750X#sh vlan
VLAN Name                             Status    Ports
---- -------------------------------- --------- -------------------------------
1    default                          active
10   VLAN0010                         active
20   VLAN0020                         active
30   VLAN0030                         active    Gi1/0/20, Gi1/0/21, Gi1/0/22, Gi2/0/20, Gi2/0/22
40   VLAN0040                         active    Gi1/0/15, Gi1/0/16, Gi1/0/17, Gi1/0/18, Gi1/0/19, Gi2/0/15, Gi2/0/16, Gi2/0/17, Gi2/0/18, Gi2/0/19
50   VLAN0050                         active    Gi1/0/1, Gi1/0/2, Gi2/0/1, Gi2/0/2
60   VLAN0060                         active    Gi1/0/5, Gi1/0/6, Gi1/0/7, Gi1/0/8, Gi1/0/9, Gi1/0/10, Gi1/0/11, Gi1/0/12, Gi1/0/13, Gi1/0/14, Gi2/0/5, Gi2/0/6, Gi2/0/7, Gi2/0/8, Gi2/0/9, Gi2/0/10, Gi2/0/11
                                                Gi2/0/12, Gi2/0/13, Gi2/0/14
100  VLAN0100                         active
101  VLAN0101                         active
102  Vlan102                          active    Gi1/0/3, Gi1/0/4, Gi2/0/3, Gi2/0/4, Gi2/0/21
1002 fddi-default                     act/unsup
1003 token-ring-default               act/unsup
1004 fddinet-default                  act/unsup
1005 trnet-default                    act/unsup

VLAN Type  SAID       MTU   Parent RingNo BridgeNo Stp  BrdgMode Trans1 Trans2
---- ----- ---------- ----- ------ ------ -------- ---- -------- ------ ------
1    enet  100001     1500  -      -      -        -    -        0      0
10   enet  100010     1500  -      -      -        -    -        0      0
20   enet  100020     1500  -      -      -        -    -        0      0
30   enet  100030     1500  -      -      -        -    -        0      0
40   enet  100040     1500  -      -      -        -    -        0      0
50   enet  100050     1500  -      -      -        -    -        0      0
60   enet  100060     1500  -      -      -        -    -        0      0
100  enet  100100     1500  -      -      -        -    -        0      0
101  enet  100101     1500  -      -      -        -    -        0      0
102  enet  100102     1500  -      -      -        -    -        0      0
1002 fddi  101002     1500  -      -      -        -    -        0      0
1003 tr    101003     1500  -      -      -        -    srb      0      0
1004 fdnet 101004     1500  -      -      -        ieee -        0      0
1005 trnet 101005     1500  -      -      -        ibm  -        0      0

"sho arp dyn int g2/0/21" is not a valid command.

#1 you are correct I am blind
#2 ping x.x.x.x source vlan 102
#3 sorry again thinking to fast it is sho mac add dyna int g2/0/21

Also, any particular reason for this?

hostname ColoC3750X

!
interface Vlan40
 ip address 10.2.4.14 255.255.255.0
!
interface Vlan50
 ip address 10.2.5.14 255.255.255.0
!
interface Vlan60
 ip address 10.2.6.14 255.255.255.0
!
interface Vlan100
 ip address 10.2.0.199 255.255.255.0

hostname Winston-3750sw

!
interface Vlan40
 ip address 10.2.4.1 255.255.255.0
!
interface Vlan50
 ip address 10.2.5.1 255.255.255.0
!
interface Vlan60
 ip address 10.2.6.1 255.255.255.0
!
interface Vlan100
 ip address 10.2.0.1 255.255.255.0

I mean, except wasting few IP addresses?
If hosts are not configured to use both SVIs as default gateway (distribute traffic load between switches or whatever) it just creates confusion.

The DMZ2 interface on firewall was newly created so no rules at all. As the result, no incoming traffic allowed. That is why.
Thanks you guys.