Are my seeds dead?

Forgive the extreme newbie-ness of this question, I have never grown anything that required early starting and I'm a veggie beginner in general.

I started tomatoes and peppers about 4 weeks ago. When the temps swung warm I put them out in my greenhouse shed, thinking it would be warm enough, and then of course it snapped back cold...again...and again... And I kept foolishly thinking "SURELY it will stay warm this time, there's no sense in lugging them all back in..."

Obviously that was a mistake, it definitely has not been warm enough for them out in the greenhouse shed. I actually didn't realize until I started reading (troubleshootinf) just how warm they actually need the soil - warmer than I thought. Result: nothing has sprouted.

Questions:
Are the seeds just plain dead by now?
Can they be rescued if I move them somewhere consistently warm?
Is it even worth trying to rescue them if they won't have a long enough growing season at this point?
Can I keep them in my oven with the light on to generate a nice hot environment? What are other good warm zones in the home? I have a big south facing window, but like the greenhouse shed I worry that it's not consistent enough... (Grow lights or heating pads are not an option.)

Thanks for any advice. I'm kind of bummed that we might be out of luck on these particular crops this year, but live and learn. I'd love to give them a second chance this year if possible.

It depends.

Lots of seeds when planted and it's too cold for them will simply stay dormant until the soil warms up. When the conditions are right for them they'll sprout. Some folks take advantage of this on purpose and plant their seeds in the winter...google winter sowing. This doesn't work with everything and often works best with perennials and flowers.

Peppers and tomatoes don't do well in cold soils and if the soil is really wet they might just rot before it gets warm enough for them to sprout.

Another problem could be if the soil warms up enough to start the sprouting process but then if gets really cold again it could kill off the tiny sprouts. So if they're in a place where it's getting warm and then cold again and then warm, and so on this isn't the best situation for them.

I'd try to keep them inside somewhere that it can stay consistently warm until they've sprouted and grown a few set of leaves. At this point you can acclimate them to outside or greenhouse conditions.

If you bring in your plants now there is a good chance at least some of them will still sprout. You could try the stove for a few days and then once you start seeing green move them to the window. IF you can make some type of mini cold frame or covering that could help keep the temperatures a bit warmer and more even for the seedlings. Just make sure you take it off and let them get some airflow during the day.

I'm not sure what your growing season is but you'll have to figure out based on timing if it's still worth it for you to try and get these plants to sprout.

Em: Welcome to the wonderful world of growing vegetables.

I start seeds in an unheated greenhouse, aka. a walk in cold-frame... Temperatures at night are around 40 in the greenhouse at night, and up to 90 during the day. Germination of peppers takes about 2 weeks. Tomatoes come up in 3 days to 10 depending on variety. Things would germinate quicker if I put them in pots in a plastic bag and put them in the house at a constant 85F (in a germination chamber.)

Warm places to germinate seeds in a house are above the fridge, next to a heater vent, in front of south facing windows. In all cases beware of overheating. 80F to 95F are great temperatures. If starting them in a place without light, check on them daily and move to a lighted location as soon as they start to sprout.

I haven't even started the tomatoes yet that I'm growing for my farm. I started the peppers about a month ago. So I suppose that you have plenty of time.

No clue if your seeds are dead or not... If they've just been too cold or dry then warming them up well aughta sprout them quickly. If they have rotted from too much water, or been frozen after starting to germinate then I don't expect them to start growing... Oven with a light on seems about right for a germination chamber...

--------Edited to add----------
Cross posted with Chris Sargent... So if I'd read that first I never would have responded... And, a gold star to Chris.

Thanks! They were definitely not overwatered - under, if anything (another learning curve!) so I don't think they would be rotted. I brought them in and have them in my oven with the light on, and will move them to the top of the fridge if I need to use the oven! Hopefully I haven't done them in.

If you planted 4 weeks ago and nothing yet it's time to put some more seeds in the pots just in case.
Sprout them in a bag with a damp paper towel overnight to be sure they get started.