OSX Mavericks 10.9.3 pre-release

[[)roi(]]

I can't use Gmail at all on Apple Mail.

Granted 10.9 introduced a few new problems with Gmail; however most of these were resolved by 10.9.2 (certainly for me; bwana's issue however is still not resolved)

Historically Gmail has always been a problem re it's non compliance with IMAP standards. Many of issues experienced with gmail are not only down to Apple introduced bugs, but also to bugs introduced by Google in it's non standard implementation of the IMAP standard.

Getting past this issue; you could either consider: waiting for Apple to fix the bugs (unlikely), Google to properly comply with the IMAP standard (unlikely), for Google to properly propose / publish a new IMAP standard, or switchover to another mail provider, for example: Microsoft, Apple, Yahoo and many others certainly don't have the gmail issues.

Btw I have 2 gmail accounts, and even though it has some issues, overall I have no major restrictions in using it on a regular basis.

 

[SauRoNZA]

I've never needed to reboot anything Mac to make it work.

 

[Way69]

I don't have this issue (multiple macs); basically I never have to reboot;
Hence I think it's quite probable the problem could be specific to your network. As to the Internet not working: have you step by step analyzed where the fault resides? For example: ping router / host ip, checking if DNS is functional; nslookup or dig, tracing a route to see where the transmission is falling off, etc..
Btw I'll happily help you where I can; basically to try to isolate the underlying cause.

who is your mail provider?

As luck would have it, I actually replaced my router with a time capsule and it made no difference. I have this issue on multiple wifi networks, even when pairing with my iPhone.

Also I have a friend in amsterdam with the exact same issue on his 2013 macbook pro. So I know that its not just me.

 

[[)roi(]]

As luck would have it, I actually replaced my router with a time capsule and it made no difference. I have this issue on multiple wifi networks, even when pairing with my iPhone.

Also I have a friend in amsterdam with the exact same issue on his 2013 macbook pro. So I know that its not just me.

The offer stands for assistance; no guarantee of success, but it can't hurt to get another opinion.
PM if you'd like work through this together.