It sounds to me like your oven has a serious fault.
Disconnect it immediately and do not use it.
(Connecting it to ground should cause the fuse to blow immediately.)
The fault probably lies in the heating element (these often fail and short to ground). Your house should have a ground connection - which jurisdiction/country are you in? Most have regulations requiring a ground connection.
This is a fairly "common" issue, that typically occurs due to high resistance at the terminal. The high resistance can be caused by corrosion, or a loose connection. The high resistance causes heating, which causes higher resistance, which leads to more heating. Eventually the insulation on the wire starts to melt, and/or burn. Usually the heat will transfer through the terminal block, and into the smaller wiring in the stove. When the heat becomes too much, the smaller appliance wiring will fail and open the circuit.
In most cases this is not a super dangerous event, as the wiring is contained within the stove. However, there is a chance that this can lead to a fire in the house, especially if the cover is not properly installed.
Causes
Corrosion
Corrosion is more commonly a problem if the wiring is aluminium, though can still be a problem with copper wiring. Because stoves/cooktops/ranges draw large amounts of current, there is typically some heating of the wiring during operation. The constant heating and cooling cycles of the wiring can lead to corrosion, and/or hardening of the wiring over time. This corrosion and/or hardening increases the resistance of the wiring, which cause the heating to be worse.
Solution
Occasional inspection of the terminal block and wiring, can prevent the corrosion/hardening from getting too bad. If you notice any discoloration or corrosion, have the cord replaced. There are also conductive pastes available, that can be applied to the wiring and terminals to help prevent corrosion. While this should always be used with aluminium wiring, it may also be applied to copper wiring.
Loose Connections
This can be caused initially by not tightening the terminals to the proper torque (usually specified by the manufacturer), or over time by heating/cooling cycles. Loose or bad connections can cause arcing and/or higher resistance. As discussed before, high resistance leads to heat.
Solution
Make sure all terminals are tightened to the manufacturers specifications. It's also a good idea to tighten the terminals after a few hours of operation. As stated before, occasional inspection can also prevent this situation.
Why didn't the breaker trip?
The heating was localized to the stove\cooktop\range, so the thermal protection in the breaker would not trip. Since stoves\cooktops\ranges draw large amounts of current during normal operation, the current during the event likely didn't go high enough to cause heating in the breaker to trigger the thermal protection. It could also be that the breaker is faulty, so it should be inspected.
Is the stove scrap?
The stove may be salvageable, though you'll want to thoroughly inspect all the wiring to insure it is not damaged. Replace any damaged wiring with equivalent parts (cooking appliances use high heat resistant wiring).
If the stove is still under warranty, you'll want to contact the manufacturer to discuss your options.
Best Answer
To meet the electrical code in the U.S. (and most anywhere) all mains electrical connections must be done in an appropriate junction box that has been tested and listed for the purpose. As a rule, the terminal block and enclosure of an oven will have been tested for making connections to the oven cord. And it may be perfectly safe to add the hood cord as well since the box already meets requirements for flame retardance. For the sake of argument I'm assuming there is sufficient volume for the heat associated with the additional connection but that may not be the case. We don't need to figure this out because . . .
If controlling a hood is not a feature of the new oven then the terminal block box almost certainly wasn't tested for this application and therefore the connection would not meet your local electrical code.
The safe and correct thing to do is to wire the hood directly using an approved method (into a new or existing outlet or junction box). This may require changing or modifying the cord. If you are not comfortable doing this sort of electrical work then it makes sense to hire an electrician to do it. They would likely bill you the minimum for a house call plus materials.