Can Bernie still win after Biden took Florida and Illinois?

Theoretically yes, but practically no.

Joe Biden does not yet have a majority of delegates, and there's still enough delegates out there that Sanders could theoretically win.  But the reality is that he's not going to.  Before today, Sanders needed to get 56% of all the remaining delegates in order to win.  He hasn't gotten 56% of the delegates in any race so far.  The numbers are going to get worse after tonight.  Joe Biden got almost 40% more of the vote in Florida, the night's biggest prize.  He beat Sanders by over 20 points in Illinois.  He's projected to win Arizona too, although the final numbers aren't known yet.  With each victory Joe Biden pushed the percentage that Bernie Sanders has to win in the remaining states higher and higher.  The continuing Biden victories also seems to show that Sanders doesn't have a demographic path forward. 

Bernie can not win.

Bernie's problem is much worse than those 2 states. 

Whether or not Biden took them isn't what matters.

It's "by how much" that makes the difference.

If Biden had won by 51-49 percent, he would have still "taken" both states.  And Sanders would still be in reach by delegate count (which is what actually earns the nomination).

But he didn't.  Biden won Illinois 58-37%, taking 93 delegates to Sanders' 46.  He won Florida 62-23%, taking 130 delegates to Sanders' 48.  That's what "by how much" means.

Biden needs less than half the remaining delegates to win the nomination outright.  Sanders has only taken more than half the delegates in three contests - his home state of Vermont, North Dakota, and the Northern Mariana Islands.  For a total of 23 delegates to Biden's 13.  By contrast, Biden has taken more than half the delegates seven times.  For 483 delegates to Sanders' 211.

In contests where one or the other of them won an outright majority, Biden is up 496 to 224 in delegate count.  That really doesn't look good for Bernie.