I cannot tell you about the seeds germination for sure. But if you are doing organically, get some manure (cow, horse, sheep) and apply it around the plants, slightly mixing with the top soil. Then as you water the plants, the nutrients will go down. I am sure there are a lot of farms around SanDiego that you can find manure, at reasonable cost. Home Depot in SD area sells STEER MANURE, at one Dollar per bag(My brother in Escandido buys a lot of it)
It is organic ,obviously, and it is a bargain at that price.

I wonder if there's a problem with your compost? You should go ahead and start hitting your garden soil with a high-Nitrogen fertilizer of your choice. Perhaps treat part of the garden and leave another part untreated to see the difference.

If the compost is unfinished compost, the Nitrogen will cause it to finish and then your plants will improve.

You mention your lawn was dead when you converted it to garden. Any idea what killed it? Or did you have a green lawn and just turn it under or spray it with glyphosate (glyphosate will leave no residues to harm what you have planted, but other herbicides may)? I ask because if the lawn was already dead, whatever killed it could be affecting what you have planted.

Low soil nitrogen will not prevent your seeds from germinating, although after they come up it will certainly stunt their growth. The classic symptom of lack of nitrogen in a growing plant is yellowing and dying leaves on the lower parts of the plant while the top/newest leaves remain green Corn is an excellent indicator plant because the symptoms show up so clearly. Legumes such as peas and beans show much less problem because they host bacteria that will manufacture the nitrogen--if the bacteria are present on the seed or in the soils when planting.

What you have described of your plants suggests a couple things to check out. First, your symptoms are consistent with herbicide damage. If it is herbicide, the wide range of seeds you have planted suggest it may be broad spectrum, soil active which may be wearing off. If this is the cause, time and heavy watering will take care of the problem. Second, the symptoms would be consistent with excess salt in the soil. Seeds often don't germinate well and die of drouth after coming up because the salt prevents the plants from absorbing water. However, I have found peas to be highly sensitive to salt compared to some of the other things you planted, so if they are doing well it may not be salt. Third, your problems are consistent with lack of moisture. Fluctuating soil moisture can result in poor germination and stunted or slow growing plants. Stick your finger into the soil going in a couple inches every day or two for a week and make sure the soil is moist all the way down. You don't want it waterlogged, but you don't want it dry. You might also take a shovel and check down 6-8 inches and make sure there is moisture there. If you water frequently for short intervals with a sprinkler, the surface could be getting wet but not soaking in deeply enough to provide the plants with what they need.

I would suggest searching further for a soil testing lab. There have got to be a number of them in Calif. and Arizona with their huge ag production. The county extension service should be able to point you to a lab. Otherwise, do a search in the yellow pages for soil testing and search the net. It doesn't have to be nearby, although I think it is better if the lab serves an area with similar soils to you (warm, arid). All that is needed for a test is about a pint of soil, it can be shipped quite easily, and the basic test usually costs around $20 or less. A test will fill you in on your nitrogen levels and your salt levels. If your salt level comes back above 4 (listed as EC or mmhos), some plants will have problems, and above 6 will really cause problems.

Good Luck

San Diego County is a major agricultural center. So if they lack soil testing labs there, they send them somewhere.

You can learn just where that is if you call your county's Univ of CA Extension Service office. Typically, such phone numbers are in the White Pages, under the heading "County Offices.

Or use the USDA map here and click your way to the office info you need.
http://www.csrees.usda.gov/Extension/

Around here, a professional lab test is about $35. I suspect it might be similar where you are.

Here is a link that might be useful: USDA clickable map of Extension Serivce offices