@Roman
That guide I posted should help you. If you don't want to face issues with XAMPP you need at least a 3.0 Ghz processor and at least 8 GB of RAM.
Sorry. Misunderstanding on my side. I thought you are trying to access the Elgg site on your home computer from the lab.
Does the site get correctly displayed on the computer XAMPP runs on? If not the problem might be with the rewrite rules not being fully working (might be due to AllowOverride not set to All or RewriteBase might be necessary to be defined). If it works on the XAMPP server but not on other clients it's possible a routing issue (static vs. dynamic IPs) or a Firewall issue (see tips of RJ in the discussion topic linked above).
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