That is an APIPA address - what a client with DHCP assigns itself if it can't get an address from a DHCP server (because there isn't one, or it can't connect to it or the server has no addresses etc.).
It is non-routable, so can never access the internet. It will, by definition, never have a default gateway.
It is only ever useful where you need to get a bunch of PCs on a single network to talk to each other, with no requirement to access any other networks (e.g. the internet).
You can attempt to manually assign an IP address, subnet mask, default gateway and DNS server address - but you have to be certain that you know what they should be and you know how to assign them.
But it may still not work if there is a network failure - i.e. the PC cannot access the network. Very probable in the scenario you outline.
Or you can find out what your DHCP server is, whether or not it is working correctly with sufficient addresses etc. and why your PC is unable to access it.
As I mentioned previously, examine carefully the various levels of security at the router / firewall / DHCP server. Does it have MAC address filtering enabled? Is WEP / WPA enabled? Are there sufficient IP addresses in the DHCP scope? Is the DHCP service working?
Etc. Etc.
SD