The problem is obvious – my IP (or better IP range where my IP belongs to) is banned by someone…But who?
Today I contacted O2 support and after three calls I finally ended up on a line with a guy who seemed to be pretty knowledgeable about the possible issues (familiar with IP bans, black lists etc.) and suggested me a workaround. He suggested me to request for a fixed IP address, paid-service provided by O2, and so my IP changes and will be in different IP range than the current.
UPDATE: The workaround with the Fixed IP adress does not help. Original IP address was 83.208.91.xx, the new one (fixed IP) is 83.208.22.xx. Still I am not able to open the Twitter home! Grrrr!
C:\Data>tracert twitter.com
Tracing route to twitter.com [168.143.162.100]
over a maximum of 30 hops:
1 1 ms 3 ms 2 ms 192.168.2.1
2 8 ms 7 ms 8 ms 194.228.196.34
3 10 ms 9 ms 10 ms 88.103.203.1
4 10 ms 11 ms 9 ms 80.188.33.245
5 11 ms 10 ms 10 ms 194.228.190.2
6 11 ms 10 ms 10 ms Xe7-1-3-0-grtprana1.red.telefonica-wholesale.net.10.16.84.in-addr.arpa [84.16.10.37]
7 142 ms 17 ms 44 ms Xe10-3-0-0-grtfraix2.red.telefonica-wholesale.net [213.140.49.114]
8 17 ms 18 ms 17 ms xe3-0-0-0-grtfraix3.red.telefonica-wholesale.net [84.16.14.162]
9 18 ms 18 ms 17 ms VERIO-5-1-0-grtfraix3.red.telefonica-wholesale.net [213.140.53.242]
10 33 ms 34 ms 33 ms p64-2-2-0.r23.amstnl02.nl.bb.gin.ntt.net [129.250.3.49]
11 115 ms 105 ms 116 ms as-0.r21.asbnva01.us.bb.gin.ntt.net [129.250.2.158]
12 184 ms 186 ms 175 ms as-3.r20.snjsca04.us.bb.gin.ntt.net [129.250.2.167]
13 283 ms 211 ms * xe-1-3.r02.mlpsca01.us.bb.gin.ntt.net [129.250.5.61]
14 * 176 ms 181 ms 129.250.24.202
15 323 ms 175 ms 176 ms 128.121.150.245
16 185 ms 181 ms 181 ms 128.121.146.181
17 203 ms 247 ms 214 ms 168.143.162.100