I simply cant get this. This is my scenario: A 3560 with a couple of VLANs should have restricted access between the VLANs but free access to the internet. But, before I should do the restrictions I noticed that routing only works between VLANs, not to the internet. The 3560 can ping the Internet, and every SVI ofc. From one VLAN I can ping the other SVIs (ofc only when they are up), but somehow the SVIs dont know how to route to the Internet, even though my default route tells them how to. How do I solve this? Maybe I'm supposed to make the port that goes to the router a l3-port?
Here is some pics to make it easier to understand. Config at bottom.
The Scenario:

Sh ip cef

sh ip route

Config: (Sorry its so damn long ;P)
version 12.2
no service pad
service timestamps debug datetime msec
service timestamps log datetime msec
no service password-encryption
!
hostname Core
!
boot-start-marker
boot-end-marker
!
!
no aaa new-model
clock timezone Secret

1
system mtu routing 1500
vtp interface fastethernet0/9
ip subnet-zero
ip routing
ip name-server 4.2.2.2
ip name-server 8.8.8.8
ip name-server 4.2.2.3
no ip dhcp use vrf connected
ip dhcp binding cleanup interval 10
ip dhcp excluded-address 192.168.10.1 192.168.10.25
ip dhcp excluded-address 192.168.30.1 192.168.30.25
ip dhcp excluded-address 192.168.20.1 192.168.20.25
ip dhcp excluded-address 192.168.100.0 192.168.100.25
ip dhcp excluded-address 192.168.200.0 192.168.200.25
!
ip dhcp pool scope1
network 192.168.10.0 255.255.255.0
dns-server 4.2.2.2
default-router 192.168.10.254
lease 3
!
ip dhcp pool scope2
network 192.168.20.0 255.255.255.0
default-router 192.168.20.254
dns-server 4.2.2.2
lease 3
!
ip dhcp pool scope3
network 192.168.30.0 255.255.255.0
default-router 192.168.30.254
dns-server 4.2.2.2
lease 3
!
ip dhcp pool PUBLIC_WIFI
network 192.168.200.0 255.255.255.0
default-router 192.168.200.254
dns-server 4.2.2.2
lease 0 1
!
!
!
!
!
!
!
!
spanning-tree mode pvst
spanning-tree extend system-id
!
vlan internal allocation policy ascending
!
!
!
interface FastEthernet0/1
description LINK TO ISA AND WAN
!
interface FastEthernet0/2
switchport mode access
spanning-tree portfast
!
interface FastEthernet0/3
description PORTS TO a LAN
switchport access vlan 10
switchport mode access
!
interface FastEthernet0/4
switchport mode access
!
interface FastEthernet0/5
description LINK TO a LAN
switchport access vlan 30
switchport mode access
!
interface FastEthernet0/6
switchport mode access
!
interface FastEthernet0/7
description LINK TO a LAN
switchport access vlan 20
switchport mode access
!
interface FastEthernet0/8
switchport access vlan 100
switchport mode access
spanning-tree portfast
!
interface FastEthernet0/9
switchport access vlan 100
switchport mode access
spanning-tree portfast
!
interface FastEthernet0/10
switchport access vlan 100
switchport mode access
spanning-tree portfast
!
interface FastEthernet0/11
switchport access vlan 100
spanning-tree portfast
!
interface FastEthernet0/12
switchport access vlan 100
switchport mode access
spanning-tree portfast
!
interface GigabitEthernet0/1
!
interface Vlan1
ip address 192.168.0.254 255.255.255.0
!
interface Vlan10
ip address 192.168.10.254 255.255.255.0
!
interface Vlan20
ip address 192.168.20.254 255.255.255.0
!
interface Vlan30
ip address 192.168.30.254 255.255.255.0
!
interface Vlan100
ip address 192.168.100.254 255.255.255.0
!
interface Vlan200
ip address 192.168.200.254 255.255.255.0
!
!
router eigrp 1
eigrp stub connected summary
network 192.168.1.0
network 192.168.10.0
network 192.168.20.0
network 192.168.30.0
network 192.168.100.0
network 192.168.200.0
!
ip default-gateway 192.168.0.1
ip classless
ip route 0.0.0.0 0.0.0.0 192.168.0.1
ip http server
!
!
control-plane
!
!
line con 0
exec-timeout 999 0
logging synchronous
line vty 0 4
login
line vty 5 15
login
!
end