Hi and welcome to Just Answer!

I can't seem to figure this out...if we should sell or rent our house.
When we are talking about tax benefits - we usually mean deductions - but to claim deductions - we have to pay these expenses. So tax benefits will only reduce such expenses if paid with pre-tax funds - however expenses still have to be paid in first place. Thus - we need to consider tax benefits in conjunction with other circumstances.
1) What are the tax benefits to owning the home, even if we have not lived in the house for the last 4+ years nor have rented it out. In 2011 we paid 30k in mortgage interest, 6200k in property taxes,
If the property is your second (not primary) home - you still might be able to deduct mortgage interest and real estate taxes on schedule A. Thus your expenses - 30k in mortgage interest, 6200k in property taxes - will be paid with pre-tax dollars.

The question is - do you need that property? If you are not using the property - do you expect the property value to appreciate? Do you think that your expenses will be returned when the property will be eventually sold? In other words - does keeping the property have a sense for investment purposes?

Conversely, what would be the tax detriment if we sold it? I can't quite come up with a number.

If the property is sold - you need to determine your capital gain.

The capital gain = (selling price) - (basis)

The basis is mainly your purchase price (assuming the property was purchased) adjusted by improvements and some other expenses.

Because the property was owned more than a year - the gain will be classified as long term capital gain - taxed at reduced rate - not more than 15%.

2) If we rent out the house what are the tax implications? We still own it, pay a mortgage and insurance but does anything change with our taxes?

If you rent the property - you will have additional rental income. You will report your rental income and rental expenses on schedule E - and your rental income will be fully of partially offset by expenses.

In additional to mortgage interest and real estate taxes - there will be additional deductions which are not available for personal properties - such as insurance, utilities (if paid by you), depreciation, etc. Most likely - there will be very little (if any) additional taxable income because of renting - but rental income will help you with expenses of keeping the property.

Let me know if you need any clarification of help to estimate your possible tax liability.