98 Landrover check engine & service engine lights

I just drove from Illinois to Oregon. Upon arrival we replaced the battery and alternator bc the overcharges alternator had burned the battery out. The check engine light was on when we began the trip but couldn’t figure out why, then it turned itself off around Wyoming. When we pulled into Oregon it was on service engine. After the repairs I had hoped it would go off. It has not, and now the check engine light AND service engine light are on. WHAT THE HECK? Is this serious, and is a private mechanic better than a dealer in terms of pricing?

The check engine light means there is a trouble code or codes stored in the PCM/computer.

Some parts stores such as Autozone will retrieve the codes no charge

Write them down and post them here.

That CEL (check engine light) is just a kid in class waving her hand trying to get you attention because she has the answer. You need to have the codes read. Some places will read them for FREE. Try Autozone or Advanced Auto Parts. Get the exact code not just their translation into English and post it back here.