Will DVLA give me time to fix dead battery on untaxed car?

My MOT and road tax have run out, but my car battery is dead so I can't drive it to the MOT test centre and I cannot tax my car without MOT. I am not registered with any breakdown cover, so my brother-in-law has bought a new battery and offered to fix it for me, but the battery will not arrive until Monday (it's Saturday). Since I start a new job tomorrow I don't know my work schedule yet, plus I have uni during the week so I don't know when I'll be free to get my MOT and tax sorted. I put my car on SORN not knowing I was not allowed to keep my car parked on my road (I thought as long as I didn't drive it it would be fine), but now I've been fined. I'm afraid that if I leave it there any longer, I could be prosecuted more harshly if DVLA find out, however my situation is making it difficult to quickly get this sorted... If I called or emailed DVLA to explain my situation, would they be willing to give me a week or two to get everything sorted? I'm afraid that they'll have no mercy and tell me I'm breaching the law and I would have ended up telling on myself. Has anyone had a situation similar to this where DVLA were willing to give you time to get things sorted? I'm a very poor student and can't afford to be fined any further, I've already had to go to family to help finance the fine, battery, MOT and tax. I'm getting really stressed...