You can call AppleCare today, they're open in the US on Saturdays however because you don't state where you're located I can't vouch for your country.
You can try some fundamentals such as repairing Disk Permissions in Disk Utility, resetting the SMC and resetting the PRAM.
It also could be a simple issue with the DNS settings your ISP is using. Macs can be sensitive to these, if you are not familiar with DNS setting please read MacWorlds DNS Troubleshooting article and then make the follow change:
1. System preferences
3. Click Advanced
4. Click DNS tab
5. Click + sign
6. Add 188.8.131.52
7. Click + sign
8. Add 184.108.40.206
9. Click OK.
10. Exit System Preferences
11. Try out your iMac and report what happened.
I noticed a very similar problem with my new 21" iMac. It became a bit better after the EFI upgrade, but still I have ping timeouts to my Time Capsule. This doesn't happen with my MacBook Air or the old MacBook Pro that the iMac should replace.