Bitcoins are still there don't worry. Seems like there is no other way for you as to wait for the new wallet to synchronize fully. Then you will be able to see the actual amount and to send BTC.
If you have your BTC address (in the Core wallet navigate to: transactions - receiving address) you can easily check the balance using and explorer like https://www.blockchain.com/explorer.
I had a similar situation some time ago when I found an old BTC Core dat.wallet file. I was able to send BTC without syncing fully.
I was afraid that I will lose my BTC because I haven't checked it and sent my BTC before the wallet was fully synced. Luckily the transaction was accepted and transferred with no problems.
I would advise you to search for tutorials on how to sync the Bitcoin Core wallet with bootstrap.dat files. If this is possible then you will sync a lot faster and maybe don't need so much space.
If I find something useful I will post links here later on.
UPDATE
I just found this very nice tutorial with screens:
https://support.bitpay.com/hc/en-us/articles/115002990903-How-can-I-recover-funds-from-a-Bitcoin-Core-wallet-dat-file-without-having-the-entire-blockchain-downloaded-
You don't need to sync the Bitcoin Core wallet at all. Just follow the tutorial and you should recover your BTC quite fast. I hope this will help you further.