remote entry and check engine

just bought a '97 eddie bauer explorer. the previous owner gave me the keyless entry remote, but it doesn't work...i bought new batteries and that didnt help so it must need programing...how?

also the check engine light comes on and off at will...engine idles okay and everything else seems okay...any ideas?

Since 1996 - all new US Vehicles must have OBDII (On Board Diagnostics 2) on them. It is much better that the OBDI - OBDII can tell you that say Cylinder 4 is mis-firing or your rear oxygen sensor on the left side is bad - a much better diagnostic than the ODB1 which would tell you oxygen sensor....
Any way - Auto parts stores have started recently carrying low-cost OBDII code readers ($70 - $130)
The cheapest will read the code that is causing the "check engine" light to come on - the more expensive one needs a regular computer to read an OBDII plug in module. This module will sample the computer every 5 seconds for some user programable sensor settings and then allow you to see just what is happening. You can also read out the codes, reset the "error log" and get a chart of your vehicle speed over time. It can hold 300 hours of these readings before it "overflows" and wipes out the first hours readings - think of it as a black box. I have one and it works great.

Most part stores can also pull codes for you. and it is usually free to help in their business. When mine did that the gas cap was bad.