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According to this and this stackexchange answer and so many other resources, I can get my wallet's private key by using the
dumpprivkey command on the debug console of Bitcoin Core (Qt) and import it into another wallet like Electrum or blockchain.info or many other wallets.
So I follow the instructions to export the private key for one of my bitcoin addresses found on 'receiving addresses' of Bitcoin Core desktop application. The private key is dumped successfully, then I create a wallet on Electrum using this private key. The wallet is created successfully. The problem is it shows my balance as 0, and also in addresses tab, my bitcoin address is totally different from what I had in Bitcoin Core.
I also tried creating the wallet using the public address (watch-only address) which shows the balance correctly but as the name suggests, I cannot spend it because the wallet is created using only the public key.
I dug a little deeper and tried to create the wallet using uncompressed private key format (I used bitaddress to get the uncompressed key) but the result was exactly the same with the exact same bitcoin address which is different from my original bitcoin address.
I also tried all the steps for blockchain.info wallet, but no luck, the result was the same again.
I'm really depressed and beginning to think that I've messed up somehow and cannot transfer my bitcoins from this wallet and may try to move on and forget about it. So my question is, have I done something wrong or I should download all the transactions on my laptop to be able to transfer BTC?
One thing that I forgot to mention is that I could not download all the transactions on Bitcoin Core client because of free space limitation on my ssd. So I cannot transfer any BTC using this application.