DRAFT
If your house bank1) is dead and nothing is working we have both short-term and long-term problems. Let's start with the short term issues.
In addition to you having no power in the van, sitting at very low states of discharge is damaging to both lead (Pb) and lithium (Li) batteries. It is important to get battery voltage off the floor ASAP.
The fastest form of charging is by alternator; if you have alternator charging start the vehicle and take it for a drive.
Note: if using a plain isolator a completely dead aux battery can pull enough current to cause resets or overheating. Use other methods first then use the alternator when Vbatt comes up a bit.
Solar, if present, will often be a gentler charging method. MPPT will run normally but PWM charge controllers will be especially weak when battery voltage is lowest.
Shore power chargers are often quite weak (like 10A) but if you can stay on the charger for hours or days the battery will recover charge.
If you have or can borrow jumper cables you may be able to “jump” your house battery from the vehicle with the van running. Relatedly, a lithium jump pack meant to jumpstart the vehicle may bring the bank up high enough where you can charge normally.
Yes, your battery may be toast but there is no use replacing it until you get the underlying issues fixed. If you replace the battery with the same problems it will be murdered, too.
If you know the battery is “injured” you might choose to run it into the ground before replacing it, or while sourcing a replacement.
With lithium banks over-discharge is not the only problem that can cause the battery to stop working. The BMS can also shut down the party if temperature is too high or low, if current is too high, or if individual cell voltages are out of whack.
Some Li batteries have special devices that can be inserted into ports to reset the BMS. Most, however, use a separate charging source to tell the BMS all is well. Something like 13v and 3A is typical. Save the vigorous charging for after the underlying problem is addressed.
If the BMS shut off because of freezing temperatures it is critical to warm the battery before charging.
If the BMS shut off because of cell imbalance try charging to a lower Absorption4) voltage like 13.8v.
If the BMS shut off because of overcurrent discontinue the load that caused it.
After the underlying issue is address charge the bank gently to a normal SoC5) before charging with full force.
Now that the ship is righted again, take solace in the fact that many before you have made these same mistakes before. Vanliving is doing, and breaking stuff, and fixing it.