New email from Iconomi:

As we are preparing for the public launch of the ICONOMI Digital Assets Management Platform, we have begun with the migration of the ethbuy.iconomi.net trading platform to the new ICONOMI platform. New registrations and deposits on the ethbuy trading platform will therefore be disabled as of today. Withdrawals of EUR will be possible until 31 May 2017, while the withdrawals of ETH will be possible until the launch of the ICONOMI Digital Assets Management Platform. Any users with remaining EUR balances after this date will be able to withdraw their funds until 31. 3. 2018 through customer support. Remaining ETH balances and all user accounts will be migrated to the new ICONOMI platform.

The ICONOMI Digital Assets Management Platform will offer several fiat ramp-ups, including Cashila.

Swiscoin Swapping  is started.

For more Detail please Visit : https://bitcointalk.org/index.php?topic=1789007

They will be sending an email update tonight to investors according to Slack.

For each OUTPUT (in your example 5000), you require a signature. Each signature carries a certain amount of bytes which increase the size of your corresponding transaction. The bigger your transaction the bigger the fee. This is basic Bitcoin knowledge. I highly recommend that you calm down and start reading through the basics again. Ranting won't help you nor change anything.

Because.. you are creating another transaction to consolidate these outputs? Any kind of on-chain movement of funds requires fees, regardless of whether you're:
1) Sending to someone else.
2) Sending to yourself (be it other addresses or sweeping outputs).

Although there are several reasons not to use blockchain.info, fees aren't one of them.
You don't pay fees to blockchain.info for making Bitcoin transactions. You pay fees because you make thousands of small transactions. Considering that you own about $35k in Bitcoin, you may want to read up on how it works, especially how it works with fees and change.

TL;DR: if you don't want to pay much on fees, don't make thousands of small transactions.

To have a wallet, web based, on blockchain or any other with +35,000$ inside, i can say you have big corones. This is something i will never do. Can't even think about it  one minute. Crazy dude. You really trust them i can say. But this is one of the last place i would keep my bitcoins for such a big ammount

You're just wasting your own time and theirs. You can solve this on your own.

It's probably some weird built-in blockchain.info alert. This wouldn't/shouldn't happen in e.g. Bitcoin Core. He could just attempt sending [max_amount] to the same address a few times, indeed.

Obviously I can't say with 100% certainity that everything will move smoothly. According to other blockchain explorers, this address has ~$34. Therefore, if you improve the private key somewhere else then it should show up. Keep me posted and I'll help if you encounter some issues.

Your money isn't lost. Stop panicking.

You should do that and then attempt to consolidate the outputs.