Replace Optiplex 990 power supply with DC power supply?

No such thing.  You will need a True Sinewave Inverter.  I would also recommend a separate battery and renology solar suitcase.

a 12v battery will drain completely in 30 minutes or less.

Unless you are using a Micro version of optiplex you will be using 200W

A car battery can run pc for 30 minutes and its done.

https://www.amazon.com/Goal-Zero-Portable-Generator-Alternative/dp/B07CS9HKDL/

https://www.amazon.com/Renogy-Eclipse-Monocrystalline-Suitcase-Controller/dp/B01NADR1CI

You might be able to get some tips from a "car pc" forum or the like. What you need is a DC-DC Converter... all that Inverter business is very inefficient. 

However, I think your best bet is to switch to a smaller (and less power hungry) form-factor like a (rugged) laptop or tablet.

Latitude E6400 XFR  would be my recommendation.  It can take being dropped as well as immersed in water,  salt, fog, run outside in the surf while its raining etc.LIND makes excellent AC adapters for Dell Laptops

https://www.dell.com/en-us/shop/lind-auto-air-adapter-acdc9020-de04-power-adapter-90-watt/apd/a9902592/pc-accessories

http://www.ebay.com/itm/like/253583848688

https://www.youtube.com/watch?v=zmd6D-DB2kk

Using inverter is a good idea.

The inverter converts DC energy (battery, storage battery) to AC (220V / 50Hz sinusoidal wave). It consists of inverter bridge, control logic and filter circuit. Inverter is a DC to AC transformer, it and converter is actually a voltage inverter process. The converter converts the AC voltage of the power network to a stable 12V DC output, while the inverter converts the 12V DC voltage from the Adapter output to a high frequency high voltage AC.

Both parts also adopt the more widely used pulse width modulation (PWM) technology. Its core part is a PWM integrated controller, which uses UC3842, and the inverter uses the working voltage range of TL5001 chip .TL5001. It has an error amplifier, a regulator, an oscillator and a PWM generator with dead-time control. Low-voltage protection circuit and short-circuit protection circuit, etc.

Inverter is a bad Idea and the reason is that it will eat up your battery and leave you stranded out in the ocean as food for the sharks. Non TRUE SINE Wave Inverters are VERY inefficient.

If you want to do that I highly recommend a solar suitcase and Battery that is separate from the onboard systems.

The other issue is that the Optiplex is not Water resistant and resistant to salt fog etc. Did you miss the ("sail boat to collect various types of data")

Salt fog and Acid Rain are very real. Salt Fog (MIL-STD-810f) or Salt Spray (IEC 60512-6 test 11f) Salt solution in both is essentially identical but ASTM salt spray exposure is continuous while IEC 60068-2-52:1996, Part 2-11 - Test Kb: Salt Mist, cyclic, alternates 2 hours of salt spray exposure with a dwell period (variable according to desired Severity) in a humid environment.

 There are many reasons why mobile computers are being tested for shipboard use by military organizations and commercial transportation companies. Real-time data collection and analysis via a single device can significantly improve navigational charting, resource allocation, and the security of on-board crews and goods. Mobile computers can also centralize the tools used for on-board and ship-to-shore communications; inform crew decisions with accurate intelligence; and aid in the execution of emergency action plans.

Unfortunately, not many commercial – or even rugged – mobile computers pass the seaworthiness test. The effects of salt fog on electronic devices can be harsh. Only ultra-rugged tablet technologies that have been tested to rigorous MIL-STD-810G Salt Fog standards have the corrosion-resistant internal and external design to prevent sea air-induced failure.