Hi Puggy858,
As has been suggested before, this is almost certainly a DHCP/staticip problem.
I've given a few points which should help below:
1) I doubt there's anything wrong with the wireless adapter so I wouldn't bother getting a replacement.
2) Your connection will almost certainly work with wired ethernet cable because the default configuration of windows is to 'Obtain IP address automatically' on that interface, and the default for most home routers is to run a DHCP server.
3) a 169.x.x.x IP address is 'the address range you get when no addresses are offered by DHCP or other mechanism'
4) If you know what the IP address of your router is (typically 192.168.0.1/192.168.1.1/192.168.0.100/10.0.0.1 etc.) that will help us setup a static IP connection if DHCP isn't enabled
5) Assuming DHCP is working on your router (as it should be by default) please follow these instructions: (apologies if these directions aren't perfect as this is from memory)
a) go to control panel ->
b) network connections (classic view) ->
c) right-click your wireless adapter interface ->
d) select properties ->
e) select IPv4 from the middle window (where options are things like Client for Microsoft networks, IPv4, IPv6 etc.) ->
f) click properties ->
g) check the radio button 'Obtain IP address automatically' and the same for the DNS/nameserver radio button below ->
h) save/ok/close all these setting windows ->
i) click start menu ->
j) click run and type "cmd" ->
k) ipconfig /release ->
l) ipconfig /renew ->
m) ipconfig /all ->
n) take a screenshot and post back here
By this point I'd expect to see some 'sensible' numbers in the IP address, subnet mask and default gateway entries for your wireless adapter (and any other interfaces which are connected)
If the above doesn't work, then I'd suggest uninstalling your adapter driver, deleting all those wireless connections (your screenshot showed 'Wireless connection 5') as they could well be confusing Windows and then reinstalling your adapter from fresh (and repeat the above again if necessary)
If that doesn't work, please try to find your router's management web panel IP address and screenshot the page relating to DHCP. People here should then be able to either tell you how to setup DHCP or configure a static ip, whichever you prefer.
Hope that helps,
Michael