Hard wiring a 4-wire oven to 3-wire outlet?
Sounds like a problem, but need more info
It sounds like you had an improper hot =&gt; hot, hot =&gt; white-normally-neutral-used-as-hot and neutral+ground =&gt; ground. If that's what you actually have, then it is a messed up version of the older style (not normally allowed now, but grandfathered in for some situations if done correctly) hot/hot/neutral connection, but using a 2-wire + ground cable instead of a 3-wire cable.
If I am correct, that means:

Ground is carrying the neutral load for the 120V controls. Ground is not supposed to carry any load except under fault conditions.
Wire colors are non-standard. White is supposed to be neutral, not hot.

I am also concerned that if someone cheated on the type of cable, they may also have cheated on the size of the wires. The actual wire gauge that you need will depend on the circuit - 30A vs. 40A vs. 50A., but the typical ordinary 2-wire + ground cable is often 12 gauge for 20A or 14 gauge for 15A and definitely not safe for 30A or more.
Before doing anything else, you need to find out the actual circuit requirements for the new oven. Check the oven manual - and post the model # here so we can take a look too. Then check the breaker or fuse to see if it meets those requirements. It needs to be big enough - to avoid nuisance trips - but not any bigger than it is supposed to be, so that it can provide the proper protection.
Whether or not the breaker is correct, I have a feeling you will need a new 4-wire (hot/hot/neutral/ground) cable to replace the existing cable. There is a possibility that a 3-wire connection (hot/hot/ground) may be OK, but we can't tell without more information.
If the existing 3-wire cable (2 insulated wires + ground) is sufficient, then the question is whether it is thick enough. You can check a wire chart, but the key numbers are typically:

15A - 14 gauge
20A - 12 gauge
30A - 10 gauge
40A - 8 gauge
50A - 6 gauge

There should be markings on the existing cable, or measure the wire directly.
Using a high-current breaker with wire that is not rated for that current is against code and DANGEROUS.