Hi and welcome to Just Answer!
The first step is to contact your broker and verify number of shares and dates these shares were granted.
Most likely - if shares were vested - the fair market value was included into your income at the time of vesting - and that may be used as your basis. If you purchased shared below the FMV - the difference should be included into your taxable wages - so you may use the FMV as your basis.
Here is historical prices for the period (1993 -2001) you received shares - http://finance.yahoo.com/q/hp?s=INTC&a=00&b=1&c=1993&d=11&e=31&f=2001&g=d
I am attaching that information here for your convenience - Intel Corporation (INTC).xls
You also need to consider reinvested dividends that are also added to the basis.
and received stocks - see here - http://finance.yahoo.com/q/hp?s=INTC&a=00&b=1&c=1993&d=11&e=31&f=2001&g=v
Unfortunately - the most important part - re-created a record of purchases and number of shares - you would need to do on your own if your broker doesn't retain these records.
Let me know if you need any clarification.
There is no magic...
If you expect me to have a record of your purchase dates and number of shares - let be honest - your expectation are unrealistic.
Only you and your broker who recorded transaction may have such records.
As you do not keep records - your only chance is to contact the broker.
If you already contacted the broker and there is no records - you are out of luck - and may do your best to re-create these lost records.
When you will have a list - at least approximated - with purchase dates and number of shares - you may use historical prices I posted above to calculate your basis.
I completely understand your frustrations - and if the answer has no value for you - you may simply ignore it.
However - if you need any clarification or help with other tax related issues - you are welcome to keep posting.